11.3: Angular Momentum
- Describe the vector nature of angular momentum
- Find the total angular momentum and torque about a designated origin of a system of particles
- Calculate the angular momentum of a rigid body rotating about a fixed axis
- Calculate the torque on a rigid body rotating about a fixed axis
- Use conservation of angular momentum in the analysis of objects that change their rotation rate
Why does Earth keep on spinning? What started it spinning to begin with? Why doesn’t Earth’s gravitational attraction not bring the Moon crashing in toward Earth? And how does an ice skater manage to spin faster and faster simply by pulling her arms in? Why does she not have to exert a torque to spin faster?
The answer to these questions is that just as the total linear motion (momentum) in the universe is conserved, so is the total rotational motion conserved. We call the total rotational motion angular momentum, the rotational counterpart to linear momentum. In this chapter, we first define and then explore angular momentum from a variety of viewpoints. First, however, we investigate the angular momentum of a single particle. This allows us to develop angular momentum for a system of particles and for a rigid body.
Angular Momentum of a Single Particle
Figure \(\PageIndex{1}\) shows a particle at a position \(\vec{r}\) with linear momentum \(\vec{p}\) = m\(\vec{v}\) with respect to the origin. Even if the particle is not rotating about the origin, we can still define an angular momentum in terms of the position vector and the linear momentum.
The angular momentum \(\vec{l}\) of a particle is defined as the cross-product of \(\vec{r}\) and \(\vec{p}\), and is perpendicular to the plane containing \(\vec{r}\) and \(\vec{p}\):
\[\vec{l} = \vec{r} \times \vec{p} \ldotp \label{11.5}\]
The intent of choosing the direction of the angular momentum to be perpendicular to the plane containing \(\vec{r}\) and \(\vec{p}\) is similar to choosing the direction of torque to be perpendicular to the plane of \(\vec{r}\) and \(\vec{F}\), as discussed in Fixed-Axis Rotation . The magnitude of the angular momentum is found from the definition of the cross-product,
\[l = rp \sin \theta,\]
where \(\theta\) is the angle between \(\vec{r}\) and \(\vec{p}\). The units of angular momentum are kg • m 2 /s. As with the definition of torque, we can define a lever arm \(r_\perp\) that is the perpendicular distance from the momentum vector \(\vec{p}\) to the origin, \(r_\perp = r \sin \theta\). With this definition, the magnitude of the angular momentum becomes
\[l = r_{\perp} p = r_{\perp} mv \ldotp\]
We see that if the direction of \(\vec{p}\) is such that it passes through the origin, then \(\theta\) = 0, and the angular momentum is zero because the lever arm is zero. In this respect, the magnitude of the angular momentum depends on the choice of origin. If we take the time derivative of the angular momentum, we arrive at an expression for the torque on the particle:
\[ \begin{align*} \frac{d \vec{l}}{dt} &= \frac{d \vec{r}}{dt} \times \vec{p} + \vec{r} \times \frac{d \vec{p}}{dt} \\[4pt] &= \vec{v} \times m \vec{v} + \vec{r} \times \frac{d \vec{p}}{dt} \\[4pt] &= \vec{r} \times \frac{d \vec{p}}{dt} \ldotp \end{align*}\]
Here we have used the definition of \(\vec{p}\) and the fact that a vector crossed into itself is zero. From Newton’s second law \(\frac{d \vec{p}}{dt} = \sum \vec{F}\), the net force acting on the particle, and the definition of the net torque, we can write
\[\frac{d \vec{l}}{dt} = \sum \vec{\tau} \ldotp \label{11.6}\]
Note the similarity with the linear result of Newton’s second law, \(\frac{d \vec{p}}{dt} = \sum \vec{F}\). The following problem-solving strategy can serve as a guideline for calculating the angular momentum of a particle.
- Choose a coordinate system about which the angular momentum is to be calculated.
- Write down the radius vector to the point particle in unit vector notation.
- Write the linear momentum vector of the particle in unit vector notation.
- Take the cross product \(\vec{l} = \vec{r} \times \vec{p}\) and use the right-hand rule to establish the direction of the angular momentum vector.
- See if there is a time dependence in the expression of the angular momentum vector. If there is, then a torque exists about the origin, and use \(\frac{d \vec{l}}{dt} = \sum \vec{\tau}\) to calculate the torque. If there is no time dependence in the expression for the angular momentum, then the net torque is zero.
A meteor enters Earth’s atmosphere (Figure \(\PageIndex{2}\)) and is observed by someone on the ground before it burns up in the atmosphere. The vector \(\vec{r}\) = 25 km \(\hat{i}\) + 25 km \(\hat{j}\) gives the position of the meteor with respect to the observer. At the instant the observer sees the meteor, it has linear momentum \(\vec{p}\) = (15.0 kg)(−2.0 km/s \(\hat{j}\)), and it is accelerating at a constant 2.0 m/s 2 (\(− \hat{j}\)) along its path, which for our purposes can be taken as a straight line.
- What is the angular momentum of the meteor about the origin, which is at the location of the observer?
- What is the torque on the meteor about the origin?
Strategy
We resolve the acceleration into x- and y-components and use the kinematic equations to express the velocity as a function of acceleration and time. We insert these expressions into the linear momentum and then calculate the angular momentum using the cross-product. Since the position and momentum vectors are in the xy-plane, we expect the angular momentum vector to be along the z-axis. To find the torque, we take the time derivative of the angular momentum.
Solution
The meteor is entering Earth’s atmosphere at an angle of 90.0° below the horizontal, so the components of the acceleration in the x- and y-directions are
\[a_{x} = 0,\; a_{y} = -2.0\; m/s^{2} \ldotp \nonumber\]
We write the velocities using the kinematic equations.
\[v_{x} = 0,\; v_{y} = (-2.0 \times 10^{3}\; m/s) - (2.0\; m/s^{2})t \ldotp \nonumber\]
- The angular momentum is \[\begin{split} \vec{l} & = \vec{r} \times \vec{p} = (25.0\; km\; \hat{i} + 25.0\; km\; \hat{j}) \times (15.0\; kg)(0 \hat{i} + v_{y} \hat{j}) \\ & = 15.0\; kg [ 25.0\; km (v_{y}) \hat{k}] \\ & = 15.0\; kg \{ (2.50 \times 10^{4}\; m)[(-2.0 \times 10^{3}\; m/s) - (2.0\; m/s^{2})t] \hat{k} \} \ldotp \end{split} \nonumber\] At t = 0, the angular momentum of the meteor about the origin is \[\vec{l}_{0} = 15.0\; kg [ (2.50 \times 10^{4}\; m)(-2.0 \times 10^{3}\; m/s) \hat{k}] = 7.50 \times 10^{8}\; kg\; \cdotp m^{2}/s (- \hat{k}) \ldotp \nonumber\] This is the instant that the observer sees the meteor.
- To find the torque, we take the time derivative of the angular momentum. Taking the time derivative of \(\vec{l}\) as a function of time, which is the second equation immediately above, we have \[\frac{d \vec{l}}{dt} = (-15.0\; kg)(2.50 \times 10^{4}\; m)(2.0\; m/s^{2}) \hat{k} \ldotp \nonumber\] Then, since \(\frac{d \vec{l}}{dt} = \sum \vec{\tau}\), we have \[\sum \vec{\tau} = -7.5 \times 10^{5}\; N\; \cdotp m\; \hat{k} \ldotp \nonumber\] The units of torque are given as newton-meters, not to be confused with joules. As a check, we note that the lever arm is the x-component of the vector \(\vec{r}\) in Figure \(\PageIndex{2}\) since it is perpendicular to the force acting on the meteor, which is along its path. By Newton’s second law, this force is $$\vec{F} = ma (- \hat{j}) = (15.0\; kg)(2.0\; m/s^{2})(- \hat{j}) = 30.0\; kg\; \cdotp m/s^{2} (- \hat{j}) \ldotp$$The lever arm is $$\vec{r}_{\perp} = 2.5 \times 10^{4}\; m\; \hat{i} \ldotp$$Thus, the torque is $$\begin{split} \sum \vec{\tau} = \vec{r}_{\perp} \times \vec{F} & = (2.5 \times 10^{4}\; m\; \hat{i}) \times (-30.0\; kg\; \cdotp m/s^{2}\; \hat{j}), \\ & = 7.5 \times 10^{5}\; N\; \cdotp m (- \hat{k}) \ldotp \end{split}$$
Significance
Since the meteor is accelerating downward toward Earth, its radius and velocity vector are changing. Therefore, since \(\vec{l} = \vec{r} \times \vec{p}\), the angular momentum is changing as a function of time. The torque on the meteor about the origin, however, is constant, because the lever arm \(\vec{r}_{\perp}\) and the force on the meteor are constants. This example is important in that it illustrates that the angular momentum depends on the choice of origin about which it is calculated. The methods used in this example are also important in developing angular momentum for a system of particles and for a rigid body.
A proton spiraling around a magnetic field executes circular motion in the plane of the paper, as shown below. The circular path has a radius of 0.4 m and the proton has velocity 4.0 x 10 6 m/s. What is the angular momentum of the proton about the origin?
Angular Momentum of a System of Particles
The angular momentum of a system of particles is important in many scientific disciplines, one being astronomy. Consider a spiral galaxy, a rotating island of stars like our own Milky Way. The individual stars can be treated as point particles, each of which has its own angular momentum. The vector sum of the individual angular momenta give the total angular momentum of the galaxy. In this section, we develop the tools with which we can calculate the total angular momentum of a system of particles.
In the preceding section, we introduced the angular momentum of a single particle about a designated origin. The expression for this angular momentum is \(\vec{l} = \vec{r} \times \vec{p}\), where the vector \(\vec{r}\) is from the origin to the particle, and \(\vec{p}\) is the particle’s linear momentum. If we have a system of N particles, each with position vector from the origin given by \(\vec{r}_{i}\) and each having momentum \(\vec{p}_{i}\), then the total angular momentum of the system of particles about the origin is the vector sum of the individual angular momenta about the origin. That is,
\[\vec{L} = \vec{l}_{1} + \vec{l}_{2} + \cdots + \vec{l}_{N} \ldotp \label{11.7}\]
Similarly, if particle i is subject to a net torque \(\vec{\tau_{i}}\) about the origin, then we can find the net torque about the origin due to the system of particles by differentiating Equation 11.7:
\[\frac{d \vec{L}}{dt} = \sum_{i} \frac{d \vec{l}_{i}}{dt} = \sum_{i} \tau_{i} \ldotp\]
The sum of the individual torques produces a net external torque on the system, which we designate \(\sum \vec{\tau}\). Thus,
\[\frac{d \vec{L}}{dt} = \sum_{i} \tau_{i} \ldotp \label{11.8}\]
Equation \ref{11.8} states that the rate of change of the total angular momentum of a system is equal to the net external torque acting on the system when both quantities are measured with respect to a given origin . Equation \ref{11.8} can be applied to any system that has net angular momentum, including rigid bodies, as discussed in the next section.
Referring to Figure \(\PageIndex{1a}\):
- Determine the total angular momentum due to the three particles about the origin.
- What is the rate of change of the angular momentum?
Strategy
Write down the position and momentum vectors for the three particles. Calculate the individual angular momenta and add them as vectors to find the total angular momentum. Then do the same for the torques.
Solution
- Particle 1: $$\vec{r}_{1} = -2.0\; m\; \hat{i} + 1.0\; m\; \hat{j},\; \vec{p}_{1} = (2.0 \; kg)(4.0\; m/s\; \hat{j}) = 8.0\; kg\; \cdotp m/s \; \hat{j},$$ $$\vec{l}_{1} = \vec{r}_{1} \times \vec{p}_{1} = -16.0\; kg\; \cdotp m^{2}/s\; \hat{k} \ldotp$$ Particle 2: $$\vec{r}_{2} = 4.0\; m \; \hat{i} + 1.0\; m\; \hat{j},\; \vec{p}_{2} = (4.0\; kg)(5.0\; m/s\; \hat{i}) = 20.0\; kg\; \cdotp m/s\; \hat{i},$$ $$\vec{l}_{2} = \vec{r}_{2} \times \vec{p}_{2} = -20.0\; kg\; \cdotp m^{2}/s\; \hat{k} \ldotp$$Particle 3: $$\vec{r}_{3} = 2.0\; m\; \hat{i} - 2.0\; m\; \hat{j},\; \vec{p}_{3} = (1.0\; kg)(3.0\; m/s\; \hat{i}) = 3.0\; kg\; \cdotp m/s\; \hat{j},$$ $$\vec{l}_{3} = \vec{r}_{3} \times \vec{p}_{3} = 6.0\; kg\; \cdotp m^{2}/s\; \hat{k} \ldotp$$We add the individual angular momenta to find the total about the origin: $$\vec{l}_{T} = \vec{l}_{1} + \vec{l}_{2} + \vec{l}_{3} = -30\; kg\; \cdotp m^{2}/s\; \hat{k} \ldotp$$
- The individual forces and lever arms are $$\begin{split} \vec{r}_{1 \perp} & = 1.0\; m\; \hat{j}, \; \vec{F}_{1} = -6.0\; N\; \hat{i},\; \vec{\tau}_{1} = 6.0\; N\; \cdotp m\; \hat{k} \\ \vec{r}_{2 \perp} & = 4.0\; m\; \hat{i}, \; \vec{F}_{2} = 10.0\; N\; \hat{i},\; \vec{\tau}_{2} = 40.0\; N\; \cdotp m\; \hat{k} \\ \vec{r}_{3 \perp} & = 2.0\; m\; \hat{j}, \; \vec{F}_{3} = -8.0\; N\; \hat{j},\; \vec{\tau}_{3} = -16.0\; N\; \cdotp m\; \hat{k} \ldotp \end{split}$$Therefore: $$\sum_{i} \vec{\tau}_{i} = \vec{\tau}_{1} + \vec{\tau}_{2} + \vec{\tau}_{3} = 30\; N\; \cdotp m\; \hat{k} \ldotp$$
Significance
This example illustrates the superposition principle for angular momentum and torque of a system of particles. Care must be taken when evaluating the radius vectors \(\vec{r}_{i}\) of the particles to calculate the angular momenta, and the lever arms, \(\vec{r}_{i \perp}\) to calculate the torques, as they are completely different quantities.
Angular Momentum of a Rigid Body
We have investigated the angular momentum of a single particle, which we generalized to a system of particles. Now we can use the principles discussed in the previous section to develop the concept of the angular momentum of a rigid body. Celestial objects such as planets have angular momentum due to their spin and orbits around stars. In engineering, anything that rotates about an axis carries angular momentum, such as flywheels, propellers, and rotating parts in engines. Knowledge of the angular momenta of these objects is crucial to the design of the system in which they are a part.
To develop the angular momentum of a rigid body, we model a rigid body as being made up of small mass segments, \(\Delta\)m i . In Figure \(\PageIndex{4}\), a rigid body is constrained to rotate about the z-axis with angular velocity \(\omega\). All mass segments that make up the rigid body undergo circular motion about the z-axis with the same angular velocity. Part (a) of the figure shows mass segment \(\Delta\)m i with position vector \(\vec{r}_{i}\) from the origin and radius R i to the z-axis. The magnitude of its tangential velocity is v i = R i \(\omega\). Because the vectors \(\vec{v}_{i}\) and \(\vec{r}_{i}\) are perpendicular to each other, the magnitude of the angular momentum of this mass segment is
\[l_{i} = r_{i} (\Delta mv_{i}) \sin 90^{o} \ldotp\]
Using the right-hand rule, the angular momentum vector points in the direction shown in Figure \(\PageIndex{4b}\). The sum of the angular momenta of all the mass segments contains components both along and perpendicular to the axis of rotation. Every mass segment has a perpendicular component of the angular momentum that will be cancelled by the perpendicular component of an identical mass segment on the opposite side of the rigid body. Thus, the component along the axis of rotation is the only component that gives a nonzero value when summed over all the mass segments. From part (b), the component of \(\vec{l}_{i}\) along the axis of rotation is
\[\begin{split} (l_{i})_{z} & = l_{i} \sin \theta_{i} = (r_{i} \Delta m_{i} v_{i}) \sin \theta_{i}, \\ & = (r_{i} \sin \theta_{i})(\Delta m_{i} v_{i}) = R_{i} \Delta m_{i} v_{i} \ldotp \end{split}\]
The net angular momentum of the rigid body along the axis of rotation is
\[L = \sum_{i} (\vec{l}_{i})_{z} = \sum_{i} R_{i} \Delta m_{i} v_{i} = \sum_{i} R_{i} \Delta m_{i} (R_{i} \omega) = \omega \sum_{i} \Delta m_{i} (R_{i})^{2} \ldotp\]
The summation \(\sum_{i} \Delta\)(R i ) 2 is simply the moment of inertia I of the rigid body about the axis of rotation. For a thin hoop rotating about an axis perpendicular to the plane of the hoop, all of the R i ’s are equal to R so the summation reduces to R 2 \(\sum_{i} \Delta\)m i = mR 2 , which is the moment of inertia for a thin hoop found in Figure 10.20. Thus, the magnitude of the angular momentum along the axis of rotation of a rigid body rotating with angular velocity \(\omega\) about the axis is
\[L = I \omega \ldotp \label{11.9}\]
This equation is analogous to the magnitude of the linear momentum p = mv. The direction of the angular momentum vector is directed along the axis of rotation given by the right-hand rule.
A robot arm on a Mars rover like Curiosity shown in Figure \(\PageIndex{5}\) is 1.0 m long and has forceps at the free end to pick up rocks. The mass of the arm is 2.0 kg and the mass of the forceps is 1.0 kg (Figure \(\PageIndex{5}\)). The robot arm and forceps move from rest to \(\omega\) = 0.1\(\pi\) rad/s in 0.1 s. It rotates down and picks up a Mars rock that has mass 1.5 kg. The axis of rotation is the point where the robot arm connects to the rover.
- What is the angular momentum of the robot arm by itself about the axis of rotation after 0.1 s when the arm has stopped accelerating?
- What is the angular momentum of the robot arm when it has the Mars rock in its forceps and is rotating upwards?
- When the arm does not have a rock in the forceps, what is the torque about the point where the arm connects to the rover when it is accelerating from rest to its final angular velocity?
Strategy
We use Equation \ref{11.9} to find angular momentum in the various configurations. When the arm is rotating downward, the right-hand rule gives the angular momentum vector directed out of the page, which we will call the positive z-direction. When the arm is rotating upward, the right-hand rule gives the direction of the angular momentum vector into the page or in the negative z-direction. The moment of inertia is the sum of the individual moments of inertia. The arm can be approximated with a solid rod, and the forceps and Mars rock can be approximated as point masses located at a distance of 1 m from the origin. For part (c), we use Newton’s second law of motion for rotation to find the torque on the robot arm.
Solution
- Writing down the individual moments of inertia, we have
- Robot arm: \[I_{R} = \frac{1}{3} m_{R} r^{2} = \frac{1}{3} (2.00\; kg)(1.00\; m)^{2} = \frac{2}{3}\; kg\; \cdotp m^{2} \ldotp\]
- Forceps: \[I_{F} = m_{F} r^{2} = (1.0\; kg)(1.0\; m)^{2} = 1.0\; kg\; \cdotp m^{2} \ldotp\]
- Mars rock: \[I_{MR} = m_{MR} r^{2} = (1.5\; kg)(1.0\; m)^{2} = 1.5\; kg\; \cdotp m^{2} \ldotp\]
Therefore, without the Mars rock, the total moment of inertia is
\[I_{Total} = I_{R} + I_{F} = 1.67\; kg\; \cdotp m^{2}\]
and the magnitude of the angular momentum is
\[L = I \omega = (1.67\; kg\; \cdotp m^{2})(0.1 \pi\; rad/s) = 0.17 \pi\; kg\; \cdotp m^{2}/s \ldotp\]
The angular momentum vector is directed out of the page in the \(\hat{k}\) direction since the robot arm is rotating counterclockwise.
- We must include the Mars rock in the calculation of the moment of inertia, so we have \[I_{Total} = I_{R} + I_{F} + I_{MR} = 3.17\; kg\; \cdotp m^{2}\] and \[L = I \omega = (3.17\; kg\; \cdotp m^{2})(0.1 \pi\; rad/s) = 0.32 \pi\; kg\; \cdotp m^{2}/s \ldotp\] Now the angular momentum vector is directed into the page in the \(− \hat{k}\) direction, by the right-hand rule, since the robot arm is now rotating clockwise.
- We find the torque when the arm does not have the rock by taking the derivative of the angular momentum using Equation \ref{11.8} \(\frac{d \vec{L}}{dt} = \sum \vec{\tau}\). But since L = I\(\omega\), and understanding that the direction of the angular momentum and torque vectors are along the axis of rotation, we can suppress the vector notation and find \[\frac{dL}{dt} = \frac{d (I \omega)}{dt} = I \frac{d \omega}{dt} = I \alpha = \sum \tau,\] which is Newton’s second law for rotation. Since \(\alpha = \frac{0.1 \pi\; rad/s}{0.1\; s} = \pi\; rad/s^{2}\), we can calculate the net torque: \[\sum \tau = I \alpha = (1.67\; kg\; \cdotp m^{2})(\pi\; rad/s^{2}) = 1.67 \pi\; N\; \cdotp m \ldotp\]
Significance
The angular momentum in (a) is less than that of (b) due to the fact that the moment of inertia in (b) is greater than (a), while the angular velocity is the same.
Which has greater angular momentum: a solid sphere of mass m rotating at a constant angular frequency \(\omega_{0}\) about the z-axis, or a solid cylinder of same mass and rotation rate about the z-axis?
Visit the University of Colorado’s Interactive Simulation of Angular Momentum to learn more about angular momentum.


12: Mechanisms of Microbial Genetics (Part A)
In 1954, French scientist and future Nobel laureate Jacques Monod (1910–1976) famously said, “What is true in E. coli is true in the elephant,” suggesting that the biochemistry of life was maintained throughout evolution and is shared in all forms of known life. Since Monod’s famous statement, we have learned a great deal about the mechanisms of gene regulation, expression, and replication in living cells. All cells use DNA for information storage, share the same genetic code, and use similar mechanisms to replicate and express it. Although many aspects of genetics are universally shared, variations do exist among contemporary genetic systems. We now know that within the shared overall theme of the genetic mechanism, there are significant differences among the three domains of life: Eukarya, Archaea, and Bacteria. Additionally, viruses, cellular parasites but not themselves living cells, show dramatic variation in their genetic material and the replication and gene expression processes. Some of these differences have allowed us to engineer clinical tools such as antibiotics and antiviral drugs that specifically inhibit the reproduction of pathogens yet are harmless to their hosts.
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- 12.1: What Are Genes?
- A gene is composed of DNA that is “read” or transcribed to produce an RNA molecule during the process of transcription. One major type of RNA molecule, called messenger RNA (mRNA), provides the information for the ribosome to catalyze protein synthesis in a process called translation. The processes of transcription and translation are collectively referred to as gene expression.
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- 12.2: DNA Replication
- The DNA replication process is semiconservative, which results in two DNA molecules, each having one parental strand of DNA and one newly synthesized strand. In bacteria, the initiation of replication occurs at the origin of replication, where supercoiled DNA is unwound by DNA gyrase, made single-stranded by helicase, and bound by single-stranded binding protein to maintain its single-stranded state.
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- 12.3: RNA Transcription
- During the process of transcription, the information encoded within the DNA sequence of one or more genes is transcribed into a strand of RNA, also called an RNA transcript. The resulting single-stranded RNA molecule, composed of ribonucleotides containing the bases adenine, cytosine, guanine, and uracil, acts as a mobile molecular copy of the original DNA sequence. Transcription in prokaryotes and in eukaryotes requires the DNA double helix to partially unwind in the region of RNA synthesis.
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- 12.4: Protein Synthesis (Translation)
- The synthesis of proteins consumes more of a cell’s energy than any other metabolic process. In turn, proteins account for more mass than any other macromolecule of living organisms. They perform virtually every function of a cell, serving as both functional (e.g., enzymes) and structural elements. The process of translation, or protein synthesis, the second part of gene expression, involves the decoding by a ribosome of an mRNA message into a polypeptide product.
Thumbnail: DNA Double Helix. (Public Domain; Apers0n).


5.9: Real Gases - Deviations from Ideal Behavior
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Learning Objectives
- To recognize the differences between the behavior of an ideal gas and a real gas
- To understand how molecular volumes and intermolecular attractions cause the properties of real gases to deviate from those predicted by the ideal gas law.
The postulates of the kinetic molecular theory of gases ignore both the volume occupied by the molecules of a gas and all interactions between molecules, whether attractive or repulsive. In reality, however, all gases have nonzero molecular volumes. Furthermore, the molecules of real gases interact with one another in ways that depend on the structure of the molecules and therefore differ for each gaseous substance. In this section, we consider the properties of real gases and how and why they differ from the predictions of the ideal gas law. We also examine liquefaction, a key property of real gases that is not predicted by the kinetic molecular theory of gases.
Pressure, Volume, and Temperature Relationships in Real Gases
For an ideal gas, a plot of \(PV/nRT\) versus \(P\) gives a horizontal line with an intercept of 1 on the \(PV/nRT\) axis. Real gases, however, show significant deviations from the behavior expected for an ideal gas, particularly at high pressures (Figure \(\PageIndex{1a}\)). Only at relatively low pressures (less than 1 atm) do real gases approximate ideal gas behavior (Figure \(\PageIndex{1b}\)).
Real gases also approach ideal gas behavior more closely at higher temperatures, as shown in Figure \(\PageIndex{2}\) for \(N_2\). Why do real gases behave so differently from ideal gases at high pressures and low temperatures? Under these conditions, the two basic assumptions behind the ideal gas law—namely, that gas molecules have negligible volume and that intermolecular interactions are negligible—are no longer valid.
Because the molecules of an ideal gas are assumed to have zero volume, the volume available to them for motion is always the same as the volume of the container. In contrast, the molecules of a real gas have small but measurable volumes. At low pressures, the gaseous molecules are relatively far apart, but as the pressure of the gas increases, the intermolecular distances become smaller and smaller (Figure \(\PageIndex{3}\)). As a result, the volume occupied by the molecules becomes significant compared with the volume of the container. Consequently, the total volume occupied by the gas is greater than the volume predicted by the ideal gas law. Thus at very high pressures, the experimentally measured value of PV / nRT is greater than the value predicted by the ideal gas law.
Moreover, all molecules are attracted to one another by a combination of forces. These forces become particularly important for gases at low temperatures and high pressures, where intermolecular distances are shorter. Attractions between molecules reduce the number of collisions with the container wall, an effect that becomes more pronounced as the number of attractive interactions increases. Because the average distance between molecules decreases, the pressure exerted by the gas on the container wall decreases, and the observed pressure is less than expected (Figure \(\PageIndex{4}\)). Thus as shown in Figure \(\PageIndex{2}\), at low temperatures, the ratio of \ (PV/nRT\) is lower than predicted for an ideal gas, an effect that becomes particularly evident for complex gases and for simple gases at low temperatures. At very high pressures, the effect of nonzero molecular volume predominates. The competition between these effects is responsible for the minimum observed in the \(PV/nRT\) versus \(P\) plot for many gases.
Nonzero molecular volume makes the actual volume greater than predicted at high pressures; intermolecular attractions make the pressure less than predicted.
At high temperatures, the molecules have sufficient kinetic energy to overcome intermolecular attractive forces, and the effects of nonzero molecular volume predominate. Conversely, as the temperature is lowered, the kinetic energy of the gas molecules decreases. Eventually, a point is reached where the molecules can no longer overcome the intermolecular attractive forces, and the gas liquefies (condenses to a liquid).
The van der Waals Equation
The Dutch physicist Johannes van der Waals (1837–1923; Nobel Prize in Physics, 1910) modified the ideal gas law to describe the behavior of real gases by explicitly including the effects of molecular size and intermolecular forces. In his description of gas behavior, the so-called van der Waals equation,
\[ \underbrace{ \left(P + \dfrac{an^2}{V^2}\right)}_{\text{Pressure Term}} \overbrace{(V − nb)}^{\text{Pressure Term}} =nRT \label{10.9.1} \]
a and b are empirical constants that are different for each gas. The values of \(a\) and \(b\) are listed in Table \(\PageIndex{1}\) for several common gases.
| Gas | a ((L 2 ·atm)/mol 2 ) | b (L/mol) |
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| He | 0.03410 | 0.0238 |
| Ne | 0.205 | 0.0167 |
| Ar | 1.337 | 0.032 |
| H 2 | 0.2420 | 0.0265 |
| N 2 | 1.352 | 0.0387 |
| O 2 | 1.364 | 0.0319 |
| Cl 2 | 6.260 | 0.0542 |
| NH 3 | 4.170 | 0.0371 |
| CH 4 | 2.273 | 0.0430 |
| CO 2 | 3.610 | 0.0429 |
The pressure term in Equation \(\ref{10.9.1}\) corrects for intermolecular attractive forces that tend to reduce the pressure from that predicted by the ideal gas law. Here, \(n^2/V^2\) represents the concentration of the gas (\(n/V\)) squared because it takes two particles to engage in the pairwise intermolecular interactions of the type shown in Figure \(\PageIndex{4}\). The volume term corrects for the volume occupied by the gaseous molecules.
The correction for volume is negative, but the correction for pressure is positive to reflect the effect of each factor on V and P , respectively. Because nonzero molecular volumes produce a measured volume that is larger than that predicted by the ideal gas law, we must subtract the molecular volumes to obtain the actual volume available. Conversely, attractive intermolecular forces produce a pressure that is less than that expected based on the ideal gas law, so the \(an^2/V^2\) term must be added to the measured pressure to correct for these effects.
Example \(\PageIndex{1}\)
You are in charge of the manufacture of cylinders of compressed gas at a small company. Your company president would like to offer a 4.00 L cylinder containing 500 g of chlorine in the new catalog. The cylinders you have on hand have a rupture pressure of 40 atm. Use both the ideal gas law and the van der Waals equation to calculate the pressure in a cylinder at 25°C. Is this cylinder likely to be safe against sudden rupture (which would be disastrous and certainly result in lawsuits because chlorine gas is highly toxic)?
Given: volume of cylinder, mass of compound, pressure, and temperature
Asked for: safety
Strategy:
A Use the molar mass of chlorine to calculate the amount of chlorine in the cylinder. Then calculate the pressure of the gas using the ideal gas law.
B Obtain a and b values for Cl 2 from Table \(\PageIndex{1}\). Use the van der Waals equation (\(\ref{10.9.1}\)) to solve for the pressure of the gas. Based on the value obtained, predict whether the cylinder is likely to be safe against sudden rupture.
Solution:
A We begin by calculating the amount of chlorine in the cylinder using the molar mass of chlorine (70.906 g/mol):
\[\begin{align} n &=\dfrac{m}{M} \\[4pt] &= \rm\dfrac{500\;g}{70.906\;g/mol} \\[4pt] &=7.052\;mol\nonumber \end{align} \nonumber \]
Using the ideal gas law and the temperature in kelvin (298 K), we calculate the pressure:
\[\begin{align} P &=\dfrac{nRT}{V} \\[4pt] &=\rm\dfrac{7.052\;mol\times 0.08206\dfrac{L\cdot atm}{mol\cdot K}\times298\;K}{4.00\;L} \\[4pt] &= 43.1\;atm \end{align} \nonumber \]
If chlorine behaves like an ideal gas, you have a real problem!
B Now let’s use the van der Waals equation with the a and b values for Cl 2 from Table \(\PageIndex{1}\). Solving for \(P\) gives
\[\begin{align}P&=\dfrac{nRT}{V-nb}-\dfrac{an^2}{V^2}\\&=\rm\dfrac{7.052\;mol\times0.08206\dfrac{L\cdot atm}{mol\cdot K}\times298\;K}{4.00\;L-7.052\;mol\times0.0542\dfrac{L}{mol}}-\dfrac{6.260\dfrac{L^2atm}{mol^2}\times(7.052\;mol)^2}{(4.00\;L)^2}\\&=\rm28.2\;atm\end{align} \nonumber \]
This pressure is well within the safety limits of the cylinder. The ideal gas law predicts a pressure 15 atm higher than that of the van der Waals equation.
Exercise \(\PageIndex{1}\)
A 10.0 L cylinder contains 500 g of methane. Calculate its pressure to two significant figures at 27°C using the
- ideal gas law.
- van der Waals equation.
- Answer a
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77 atm
- Answer b
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67 atm
Liquefaction of Gases
Liquefaction of gases is the condensation of gases into a liquid form, which is neither anticipated nor explained by the kinetic molecular theory of gases. Both the theory and the ideal gas law predict that gases compressed to very high pressures and cooled to very low temperatures should still behave like gases, albeit cold, dense ones. As gases are compressed and cooled, however, they invariably condense to form liquids, although very low temperatures are needed to liquefy light elements such as helium (for He, 4.2 K at 1 atm pressure).
Liquefaction can be viewed as an extreme deviation from ideal gas behavior. It occurs when the molecules of a gas are cooled to the point where they no longer possess sufficient kinetic energy to overcome intermolecular attractive forces. The precise combination of temperature and pressure needed to liquefy a gas depends strongly on its molar mass and structure, with heavier and more complex molecules usually liquefying at higher temperatures. In general, substances with large van der Waals \(a\) coefficients are relatively easy to liquefy because large a coefficients indicate relatively strong intermolecular attractive interactions. Conversely, small molecules with only light elements have small a coefficients, indicating weak intermolecular interactions, and they are relatively difficult to liquefy. Gas liquefaction is used on a massive scale to separate O 2 , N 2 , Ar, Ne, Kr, and Xe. After a sample of air is liquefied, the mixture is warmed, and the gases are separated according to their boiling points.
A large value of a in the van der Waals equation indicates the presence of relatively strong intermolecular attractive interactions.
The ultracold liquids formed from the liquefaction of gases are called cryogenic liquids, from the Greek kryo , meaning “cold,” and genes , meaning “producing.” They have applications as refrigerants in both industry and biology. For example, under carefully controlled conditions, the very cold temperatures afforded by liquefied gases such as nitrogen (boiling point = 77 K at 1 atm) can preserve biological materials, such as semen for the artificial insemination of cows and other farm animals. These liquids can also be used in a specialized type of surgery called cryosurgery , which selectively destroys tissues with a minimal loss of blood by the use of extreme cold.
Moreover, the liquefaction of gases is tremendously important in the storage and shipment of fossil fuels (Figure \(\PageIndex{5}\)). Liquefied natural gas (LNG) and liquefied petroleum gas (LPG) are liquefied forms of hydrocarbons produced from natural gas or petroleum reserves. LNG consists mostly of methane, with small amounts of heavier hydrocarbons; it is prepared by cooling natural gas to below about −162°C. It can be stored in double-walled, vacuum-insulated containers at or slightly above atmospheric pressure. Because LNG occupies only about 1/600 the volume of natural gas, it is easier and more economical to transport. LPG is typically a mixture of propane, propene, butane, and butenes and is primarily used as a fuel for home heating. It is also used as a feedstock for chemical plants and as an inexpensive and relatively nonpolluting fuel for some automobiles.
Summary
No real gas exhibits ideal gas behavior, although many real gases approximate it over a range of conditions. Deviations from ideal gas behavior can be seen in plots of PV / nRT versus P at a given temperature; for an ideal gas, PV / nRT versus P = 1 under all conditions. At high pressures, most real gases exhibit larger PV / nRT values than predicted by the ideal gas law, whereas at low pressures, most real gases exhibit PV / nRT values close to those predicted by the ideal gas law. Gases most closely approximate ideal gas behavior at high temperatures and low pressures. Deviations from ideal gas law behavior can be described by the van der Waals equation , which includes empirical constants to correct for the actual volume of the gaseous molecules and quantify the reduction in pressure due to intermolecular attractive forces. If the temperature of a gas is decreased sufficiently, liquefaction occurs, in which the gas condenses into a liquid form. Liquefied gases have many commercial applications, including the transport of large amounts of gases in small volumes and the uses of ultracold cryogenic liquids .


9.5: Rehabilitation Versus Restorative Care
As previously explained in “The Rehabilitation Process” section, speech therapists, occupational therapists, and physical therapists create the client’s rehabilitation plan with the goal of returning them to their level of function prior to the injury or illness. When an individual has progressed to their highest level of functioning, a restorative care plan is established to ensure this level of function is maintained. Although therapists provide rehabilitation therapy, nursing assistants are responsible for providing restorative care planned by the therapy team.
Common restorative plans include assisting with ambulation ( Chapter 8.5 ); performing passive or active range-of-motion (ROM) exercises ( Chapter 9.6 ); assisting with activities of daily living (ADLs) ( Chapter 5.2 ); and applying prosthetics, splints, and orthotics ( Chapter 8.6 ). Providing restorative care should be documented because it is an integral part of keeping residents as independent as possible and maintaining their overall health and quality of life. If the client resides in a facility that receives Medicare reimbursement, restorative care is reported as part of the person’s quarterly minimum data set (MDS) assessment. (To review aspects of MDS, see Chapter 1.5, “ Documenting and Reporting .”) If it is found that a resident experienced a decline in mobility because their restorative care plan was not being followed appropriately, the facility must provide therapy at no charge to restore their prior level of function.
Restorative care can occur individually or within a group. An individual activity means the nursing assistant is working with one resident at a time on that resident’s specific restorative needs. Restorative care can also occur in a group setting, such as an exercise group where residents follow the lead of an aide and participate as they are able. As discussed in the Chapter 8.6, “ Applying Prosthetics and Orthotics ” section, it is the nursing assistant’s responsibility to know how to properly perform restorative care, as well as keep residents safe from injury during restorative activities. If you are unsure about any aspect of restorative care, seek instruction from your supervising nurse.
Although clients benefit from restorative care and are encouraged to participate, they do have the right to refuse to participate in restorative care, just as they do in any other aspect of their health care. Certain situations, such as those described below, can make it difficult to motivate residents to participate in restorative care [1] :
- The resident has cognitive deficits that make the benefits of restorative care difficult to understand or impair their ability to participate.
- The resident has been dependent on others for their daily care for a long time.
- The resident experiences pain associated with the activity.
- The resident (or their caregiver) is fearful of falling or becoming injured when performing the activity.
- There is unfamiliarity or the lack of a trusting relationship between the caregiver and resident.
If these circumstances occur, the nursing assistant should continue to encourage the resident to participate in the restorative care in a respectful manner. It may be helpful to delay the care and reapproach the resident at a different time of day. If the resident displays any subjective or objective signs of pain, it should be reported to the nurse for assessment and treatment. Involving loved ones in explaining the importance of restorative care can also enhance a resident’s participation, along with reassurance from a nurse or therapist who oversees the restorative plan. If the resident continues to decline participation despite these attempted approaches, the nursing assistant should report the situation to the nurse, as well as document it was the resident’s choice to not participate in restorative care activities despite the approaches attempted.
For more information on restorative care, see Restorative Care’s Effect on Activities of Daily Living Dependency in Long-stay Nursing Home Residents .
- Talley, K. M., Wyman, J. F., Savik, K., Kane, R. L., Mueller, C., & Zhao, H. (2015). Restorative care's effect on activities of daily living dependency in long-stay nursing home residents. The Gerontologist, 55 (Supplement 1), S88–S98. https://doi.org/10.1093/geront/gnv011 ↵


1.2: The Sociological Imagination
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Learning Objectives
- Discuss C. Wright Mills’ claim concerning the importance of the “sociological imagination” for individuals
The Sociological Imagination
Early sociological theorists, like Marx, Weber, and Durkheim, were concerned with the phenomena they believed to be driving social change in their time. Naturally, in pursuing answers to these large questions, they received intellectual stimulation. These founders of sociology were some of the earliest individuals to employ what C. Wright Mills (a prominent mid-20 th century American sociologist) would later call the sociological imagination: the ability to situate personal troubles and life trajectories within an informed framework of larger social processes. The term sociological imagination describes the type of insight offered by the discipline of sociology. While scholars have quarreled over interpretations of the phrase, it is also sometimes used to emphasize sociology’s relevance in daily life.
C. Wright Mills
In describing the sociological imagination, Mills asserted the following. “What people need… is a quality of mind that will help them to use information and to develop reason in order to achieve lucid summations of what is going on in the world and of what may be happening within themselves. The sociological imagination enables its possessor to understand the larger historical scene in terms of its meaning for the inner life and the external career of a variety of individuals. ” Mills believed in the power of the sociological imagination to connect “personal troubles to public issues. ”
As Mills saw it, the sociological imagination helped individuals cope with the social world by enabling them to step outside their own, personal, self-centered view of the world. By employing the sociological imagination, individual people are forced to perceive, from an objective position, events and social structures that influence behavior, attitudes, and culture.
In the decades after Mills, other scholars have employed the term to describe the sociological approach in a more general way. Another way of defining the sociological imagination is the understanding that social outcomes are shaped by social context, actors, and actions.
Key Points
- Because they tried to understand the larger processes that were affecting their own personal experience of the world, it might be said that the founders of sociology, like Marx, Weber, and Durkheim, exercised what C. Wright Mills later called the sociological imagination.
- C. Wright Mills, a prominent mid-20th century American sociologist, described the sociological imagination as the ability to situate personal troubles and life trajectories within an informed framework of larger social processes.
- Other scholars after Mills have employed the phrase more generally, as the type of insight offered by sociology and its relevance in daily life. Another way of describing sociological imagination is the understanding that social outcomes are shaped by social context, actors, and social actions.
Key Terms
- the sociological imagination : Coined by C. Wright Mills, the sociological imagination is the ability to situate personal troubles and life trajectories within an informed framework of larger social processes.


21: Nuclear Chemistry
The chemical reactions that we have considered in previous chapters involve changes in the electronic structure of the species involved, that is, the arrangement of the electrons around atoms, ions, or molecules. Nuclear structure, the numbers of protons and neutrons within the nuclei of the atoms involved, remains unchanged during chemical reactions. This chapter will introduce the topic of nuclear chemistry, which began with the discovery of radioactivity in 1896 by French physicist Antoine Becquerel and has become increasingly important during the twentieth and twenty-first centuries, providing the basis for various technologies related to energy, medicine, geology, and many other areas.
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- 21.2: Nuclear Equations
- Nuclei can undergo reactions that change their number of protons, number of neutrons, or energy state. Many different particles can be involved in nuclear reactions. The most common are protons, neutrons, positrons (which are positively charged electrons), alpha (α) particles (which are high-energy helium nuclei), beta (β) particles (which are high-energy electrons), and gamma (γ) rays (which compose high-energy electromagnetic radiation).
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- 21.3: Radioactive Decay
- Unstable nuclei undergo spontaneous radioactive decay. The most common types of radioactivity are α decay, β decay, γ emission, positron emission, and electron capture. Nuclear reactions also often involve γ rays, and some nuclei decay by electron capture. Each of these modes of decay leads to the formation of a new stable nuclei sometimes via multiple decays before ending in a stable isotope. All nuclear decay processes follow first-order kinetics and each radioisotope has its own half-life.
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- 21.4: Transmutation and Nuclear Energy
- It is possible to produce new atoms by bombarding other atoms with nuclei or high-speed particles. The products of these transmutation reactions can be stable or radioactive. A number of artificial elements, including technetium, astatine, and the transuranium elements, have been produced in this way. Nuclear power as well as nuclear weapon detonations can be generated through fission (reactions in which a heavy nucleus is split into two or more lighter nuclei and several neutrons).
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- 21.5: Uses of Radioisotopes
- Compounds known as radioactive tracers can be used to follow reactions, track the distribution of a substance, diagnose and treat medical conditions, and much more. Other radioactive substances are helpful for controlling pests, visualizing structures, providing fire warnings, and for many other applications. Hundreds of millions of nuclear medicine tests and procedures, using a wide variety of radioisotopes with relatively short half-lives, are performed every year in the US.
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- 21.6: Biological Effects of Radiation
- We are constantly exposed to radiation from naturally occurring and human-produced sources. This radiation can affect living organisms. Ionizing radiation is the most harmful because it can ionize molecules or break chemical bonds, which damages the molecule and causes malfunctions in cell processes. Types of radiation differ in their ability to penetrate material and damage tissue, with alpha particles the least penetrating but potentially most damaging and gamma rays are most penetrating.
Contributors
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Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


6.3: Types of Locomotion
- Explain different types of locomotion with reference to environmental limitations and/or hard structure support for muscle function
The muscular and skeletal systems provide support to the body and allow for movement. The bones of the skeleton protect the body’s internal organs and support the weight of the body. The muscles of the muscular system contract and pull on the bones, allowing for movements as diverse as standing, walking, running, and grasping items. We will focus on the connection between human skeletal and muscular system to illustrate how these two organ systems coordinate to generate locomotion.
Human Skeletal System
The human skeleton is an endoskeleton that consists of 206 bones in the adult. An endoskeleton develops within the body rather than outside like the exoskeleton of insects. The skeleton has five main functions: providing support to the body, storing minerals and lipids, producing blood cells, protecting internal organs, and allowing for movement. The skeletal system in vertebrates is divided into the axial skeleton (which consists of the skull, vertebral column, and rib cage), and the appendicular skeleton (which consists of limb bones, the pectoral or shoulder girdle, and the pelvic girdle).
Explore the human skeleton by viewing the following video with digital 3D sculpturing.
The axial skeleton forms the central axis of the body and includes the bones of the skull, ossicles of the middle ear, hyoid bone of the throat, vertebral column, and the thoracic cage (rib cage) (Figure 6.5).
The bones of the skull support the structures of the face and protect the brain. The skull consists of cranial bones and facial bones. The cranial bones form the cranial cavity, which encloses the brain and serves as an attachment site for muscles of the head and neck. In the adult, they are tightly jointed with connective tissue and adjoining bones do not move.
The auditory ossicles of the middle ear transmit sounds from the air as vibrations to the fluid-filled cochlea. The auditory ossicles consist of two malleus (hammer) bones, two incus (anvil) bones, and two stapes (stirrups), one on each side. Facial bones provide cavities for the sense organs (eyes, mouth, and nose), and serve as attachment points for facial muscles.
The hyoid bone lies below the mandible in the front of the neck. It acts as a movable base for the tongue and is connected to muscles of the jaw, larynx, and tongue. The mandible forms a joint with the base of the skull. The mandible controls the opening to the mouth and hence, the airway and gut.
The vertebral column, or spinal column, surrounds and protects the spinal cord, supports the head, and acts as an attachment point for ribs and muscles of the back and neck. It consists of 26 bones: the 24 vertebrae, the sacrum, and the coccyx. Each vertebral body has a large hole in the center through which the spinal cord passes down to the level of the first lumbar vertebra. Below this level, the hole contains spinal nerves which exit between the vertebrae. There is a notch on each side of the hole through which the spinal nerves, can exit from the spinal cord to serve different regions of the body. The vertebral column is approximately 70 cm (28 in) in adults and is curved, which can be seen from a side view.
Intervertebral discs composed of fibrous cartilage lie between adjacent vertebrae from the second cervical vertebra to the sacrum. Each disc helps form a slightly moveable joint and acts as a cushion to absorb shocks from movements such as walking and running.
The thoracic cage, also known as the rib cage consists of the ribs, sternum, thoracic vertebrae, and costal cartilages. The thoracic cage encloses and protects the organs of the thoracic cavity including the heart and lungs. It also provides support for the shoulder girdles and upper limbs and serves as the attachment point for the diaphragm, muscles of the back, chest, neck, and shoulders. Changes in the volume of the thorax enable breathing. The sternum, or breastbone, is a long flat bone located at the anterior of the chest. Like the skull, it is formed from many bones in the embryo, which fuses in the adult. The ribs are 12 pairs of long curved bones that attach to the thoracic vertebrae and curve toward the front of the body, forming the ribcage. Costal cartilages connect the anterior ends of most ribs to the sternum.
The appendicular skeleton is composed of the bones of the upper and lower limbs. It also includes the pectoral, or shoulder girdle, which attaches the upper limbs to the body, and the pelvic girdle, which attaches the lower limbs to the body (Figure 6.5).
The pectoral girdle bones transfer force generated by muscles acting on the upper limb to the thorax. It consists of the clavicles (or collarbones) in the anterior, and the scapulae (or shoulder blades) in the posterior.
The upper limb contains bones of the arm (shoulder to elbow), the forearm, and the hand. The humerus is the largest and longest bone of the upper limb. It forms a joint with the shoulder and with the forearm at the elbow. The forearm extends from the elbow to the wrist and consists of two bones. The hand includes the bones of the wrist, the palm, and the bones of the fingers.
The pelvic girdle attaches to the lower limbs of the axial skeleton. Since it is responsible for bearing the weight of the body and for locomotion, the pelvic girdle is securely attached to the axial skeleton by strong ligaments. It also has deep sockets with robust ligaments that securely attach to the femur. The pelvic girdle is mainly composed of two large hip bones. The hip bones join together in the anterior of the body at a joint called the pubic symphysis and with the bones of the sacrum at the posterior of the body.
The lower limb consists of the thigh, the leg, and the foot. The bones of the lower limbs are thicker and stronger than the bones of the upper limbs to support the entire weight of the body and the forces from locomotion. The femur, or thighbone, is the longest, heaviest, and strongest bone in the body. The femur and pelvis form the hip joint. At its other end, the femur, along with the shinbone and kneecap, form the knee joint.
Joints and skeletal movement
The point at which two or more bones meet is called a joint, or articulation. Joints are responsible for movement, such as the movement of limbs, and stability, such as the stability found in the bones of the skull.
There are two ways to classify joints: based on their structure or based on their function. The structural classification divides joints into fibrous, cartilaginous, and synovial joints depending on the material composing the joint and the presence or absence of a cavity in the joint. The bones of fibrous joints are held together by fibrous connective tissue. There is no cavity, or space, present between the bones, so most fibrous joints do not move at all, or are only capable of minor movements. The joints between the bones in the skull and between the teeth and the bone of their sockets are examples of fibrous joints (Figure 6.6a).
Cartilaginous joints are joints in which the bones are connected by cartilage (Figure 6.6b). An example is found at the joints between vertebrae, the so-called “disks” of the backbone. Cartilaginous joints allow for very little movement.
Synovial joints are the only joints that have a space between the adjoining bones (Figure 6.6c). This space is referred to as the joint cavity and is filled with fluid. The fluid lubricates the joint, reducing friction between the bones and allowing for greater movement. The ends of the bones are covered with cartilage and the entire joint is surrounded by a capsule. Synovial joints are capable of the greatest movement of the joint types. Knees, elbows, and shoulders are examples of synovial joints.
The wide range of movement allowed by synovial joints produces different types of movements. Angular movements are produced when the angle between the bones of a joint changes. Flexion, or bending, occurs when the angle between the bones decreases. Moving the forearm upward at the elbow is an example of flexion. Extension is the opposite of flexion in that the angle between the bones of a joint increases. Rotational movement is the movement of a bone as it rotates around its own longitudinal axis. Movement of the head as in saying “no” is an example of rotation.
Animal Locomotion
Humans are limited to terrestrial locomotion on two limbs or swimming with all four limbs. Other animals explore both the aquatic and aerial realm more extensively. For example, birds are excellent swimmers and fliers. However, some birds are not good at moving in both air and water. One example of birds with limited abilities in flight are penguins and another are members of an extinct group Hesperirnithformes, who, just like penguins, were not able to swim in water and only had limited locomotion on land.
Watch the video about swimming locomotion in extinct Hesperornithiformes to help you understand how skeleton and muscles coordinate to generate locomotion and why some animals may be more limited in locomotion in one type of environment.
Which mode of locomotion do you think is least efficient in terms of total energy expenditure if you are considering animals of different size?


2.4: Astrology and Astronomy
By the end of this section, you will be able to:
- Explain the origins of astrology
- Explain what a horoscope is
- Summarize the arguments that invalidate astrology as a scientific practice
Many ancient cultures regarded the planets and stars as representatives or symbols of the gods or other supernatural forces that controlled their lives. For them, the study of the heavens was not an abstract subject; it was connected directly to the life-and-death necessity of understanding the actions of the gods and currying favor with them. Before the time of our scientific perspectives, everything that happened in nature—from the weather, to diseases and accidents, to celestial surprises such as eclipses or new comets—was thought to be an expression of the whims or displeasure of the gods. Any signs that helped people understand what these gods had in mind were considered extremely important.
The movements of the seven objects that had the power to “wander” through the realm of the sky—the Sun, the Moon, and five planets visible to the unaided eye—clearly must have special significance in such a system of thinking.
Most ancient cultures associated these seven objects with various supernatural rulers in their pantheon and kept track of them for religious reasons. Even in the comparatively sophisticated Greece of antiquity, the planets had the names of gods and were credited with having the same powers and influences as the gods whose names they bore. From such ideas was born the ancient system called astrology , still practiced by some people today, in which the positions of these bodies among the stars of the zodiac are thought to hold the key to understanding what we can expect from life.
The Beginnings of Astrology
Astrology began in Babylonia about two and half millennia ago. The Babylonians, believing the planets and their motions influenced the fortunes of kings and nations, used their knowledge of astronomy to guide their rulers. When the Babylonian culture was absorbed by the Greeks, astrology gradually came to influence the entire Western world and eventually spread to Asia as well.
By the 2nd century BCE the Greeks democratized astrology by developing the idea that the planets influence every individual. In particular, they believed that the configuration of the Sun, Moon, and planets at the moment of birth affected a person’s personality and fortune—a doctrine called natal astrology . Natal astrology reached its peak with Ptolemy 400 years later. As famous for his astrology as for his astronomy, Ptolemy compiled the Tetrabiblos , a treatise on astrology that remains the “bible” of the subject. It is essentially this ancient religion, older than Christianity or Islam, that is still practiced by today’s astrologers.
The Horoscope
The key to natal astrology is the horoscope , a chart showing the positions of the planets in the sky at the moment of an individual’s birth. The word “horoscope” comes from the Greek words hora (meaning “time”) and skopos (meaning a “watcher” or “marker”), so “horoscope” can literally be translated as “marker of the hour.” When a horoscope is charted, the planets (including the Sun and Moon, classed as wanderers by the ancients) must first be located in the zodiac. At the time astrology was set up, the zodiac was divided into 12 sectors called signs (Figure 2.15), each 30° long. Each sign was named after a constellation in the sky through which the Sun, Moon, and planets were seen to pass—the sign of Virgo after the constellation of Virgo, for example.
When someone today casually asks you your “sign,” they are asking for your “sun sign”—which zodiac sign the Sun was in at the moment you were born. However, more than 2000 years have passed since the signs received their names from the constellations. Because of precession, the constellations of the zodiac slide westward along the ecliptic, going once around the sky in about 26,000 years. Thus, today the real stars have slipped around by about 1/12 of the zodiac—about the width of one sign.
In most forms of astrology, however, the signs have remained assigned to the dates of the year they had when astrology was first set up. This means that the astrological signs and the real constellations are out of step; the sign of Aries, for example, now occupies the constellation of Pisces. When you look up your sun sign in a newspaper astrology column, the name of the sign associated with your birthday is no longer the name of the constellation in which the Sun was actually located when you were born. To know that constellation, you must look for the sign before the one that includes your birthday.
A complete horoscope shows the location of not only the Sun, but also the Moon and each planet in the sky by indicating its position in the appropriate sign of the zodiac. However, as the celestial sphere turns (owing to the rotation of Earth), the entire zodiac moves across the sky to the west, completing a circuit of the heavens each day. Thus, the position in the sky (or “house” in astrology) must also be calculated. There are more or less standardized rules for the interpretation of the horoscope, most of which (at least in Western schools of astrology) are derived from the Tetrabiblos of Ptolemy. Each sign, each house, and each planet—the last acting as a center of force—is supposed to be associated with particular matters in a person’s life.
The detailed interpretation of a horoscope is a very complicated business, and there are many schools of astrological thought on how it should be done. Although some of the rules may be standardized, how each rule is to be weighed and applied is a matter of judgment—and “art.” It also means that it is very difficult to tie down astrology to specific predictions or to get the same predictions from different astrologers.
Astrology Today
Astrologers today use the same basic principles laid down by Ptolemy nearly 2000 years ago. They cast horoscopes (a process much simplified by the development of appropriate computer programs) and suggest interpretations. Sun sign astrology (which you read in the newspapers and many magazines) is a recent, simplified variant of natal astrology. Although even professional astrologers do not place much trust in such a limited scheme, which tries to fit everyone into just 12 groups, sun sign astrology is taken seriously by many people (perhaps because it is discussed so commonly in the media).
Today, we know much more about the nature of the planets as physical bodies, as well as about human genetics, than the ancients could. It is hard to imagine how the positions of the Sun, Moon, or planets in the sky at the moment of our birth could have anything to do with our personality or future. There are no known forces, not gravity or anything else, that could cause such effects. (For example, a straightforward calculation shows that the gravitational pull of the obstetrician delivering a newborn baby is greater than that of Mars.) Astrologers thus have to argue there must be unknown forces exerted by the planets that depend on their configurations with respect to one another and that do not vary according to the distance of the planet—forces for which there is no shred of evidence.
Another curious aspect of astrology is its emphasis on planet configurations at birth. What about the forces that might influence us at conception? Isn’t our genetic makeup more important for determining our personality than the circumstances of our birth? Would we really be a different person if we had been born a few hours earlier or later, as astrology claims? (Back when astrology was first conceived, birth was thought of as a moment of magic significance, but today we understand a lot more about the long process that precedes it.)
Actually, very few well-educated people today buy the claim that our entire lives are predetermined by astrological influences at birth, but many people apparently believe that astrology has validity as an indicator of affinities and personality. A surprising number of Americans make judgments about people—whom they will hire, associate with, and even marry—on the basis of astrological information. To be sure, these are difficult decisions, and you might argue that we should use any relevant information that might help us to make the right choices. But does astrology actually provide any useful information on human personality? This is the kind of question that can be tested using the scientific method (see Testing Astrology).
The results of hundreds of tests are all the same: there is no evidence that natal astrology has any predictive power, even in a statistical sense. Why, then, do people often seem to have anecdotes about how well their own astrologer advised them? Effective astrologers today use the language of the zodiac and the horoscope only as the outward trappings of their craft. Mostly they work as amateur therapists, offering simple truths that clients like or need to hear. (Recent studies have shown that just about any sort of short-term therapy makes people feel a little better because the very act of talking about our problems with someone who listens attentively is, in itself, beneficial.)
The scheme of astrology has no basis in scientific fact, however; at best, it can be described as a pseudoscience. It is an interesting historical system, left over from prescientific days and best remembered for the impetus it gave people to learn the cycles and patterns of the sky. From it grew the science of astronomy, which is our main subject for discussion.
In response to modern public interest in astrology, scientists have carried out a wide range of statistical tests to assess its predictive power. The simplest of these examine sun sign astrology to determine whether—as astrologers assert—some signs are more likely than others to be associated with some objective measure of success, such as winning Olympic medals, earning high corporate salaries, or achieving elective office or high military rank. (You can devise such a test yourself by looking up the birth dates of all members of Congress, for example, or all members of the U.S. Olympic team.) Are our political leaders somehow selected at birth by their horoscopes and thus more likely to be Leos, say, than Scorpios?
You do not even need to be specific about your prediction in such tests. After all, many practitioners of astrology disagree about which signs go with which personality characteristics. To demonstrate the validity of the astrological hypothesis, it would be sufficient if the birthdays of all our leaders clustered in any one or two signs in some statistically significant way. Dozens of such tests have been performed, and all have come up completely negative: the birth dates of leaders in all fields tested have been found to be distributed randomly among all the signs. Sun sign astrology does not predict anything about a person’s future occupation or strong personality traits.
In a fine example of such a test, two statisticians examined the reenlistment records of the United States Marine Corps. We suspect you will agree that it takes a certain kind of personality not only to enlist, but also to reenlist in the Marines. If sun signs can predict strong personality traits—as astrologers claim—then those who reenlisted (with similar personalities) should have been distributed preferentially in those one or few signs that matched the personality of someone who loves being a Marine. However, the reenlisted were distributed randomly among all the signs.
More sophisticated studies have also been done, involving full horoscopes calculated for thousands of individuals. The results of all these studies are also negative: none of the systems of astrology has been shown to be at all effective in connecting astrological aspects to personality, success, or finding the right person to love.
Other tests show that it hardly seems to matter what a horoscope interpretation says, as long as it is vague enough, and as long as each subject feels it was prepared personally just for him or her. The French statistician Michel Gauquelin, for example, sent the horoscope interpretation for one of the worst mass murderers in history to 150 people, but told each recipient that it was a “reading” prepared exclusively for him or her. Ninety-four percent of the readers said they recognized themselves in the interpretation of the mass murderer’s horoscope.
Geoffrey Dean, an Australian researcher, reversed the astrological readings of 22 subjects, substituting phrases that were the opposite of what the horoscope actually said. Yet, his subjects said that the resulting readings applied to them just as often (95%) as the people to whom the original phrases were given.
For more on astrology and science from an astronomer’s point of view, read this article that shines light on the topic through an accessible Q&A.


10.2: Industrial Preparation and Use of Alkenes
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Objectives
After completing this section, you should be able to
- discuss the industrial importance of ethylene (ethene) and propylene (propene).
- describe, briefly, the industrial process known as thermal cracking.
Study Notes
Among the most important and most abundant organic chemicals produced worldwide are the two simple alkenes, ethylene and propylene. They are used as the starting materials to synthesize numerous valuable compounds.
Produced from ethylene (ethene)
| Chemical | Uses |
|---|---|
| ethanol | solvent; constituent of cleaning preparations; in synthesis of esters |
| acetaldehyde | slug killer, in the form of methaldehyde (CH 3 CHO) 4 |
| acetic acid | manufacture of vinyl acetate polymers, ethyl acetate solvent and cellulose acetate polymers |
| ethylene oxide | “cellosolves” (industrial solvents) |
| ethylene glycol | anti-freeze; production of DacronOR |
| ethylene dichloride | solvent; production of vinyl chloride |
| vinyl chloride | manufacture of poly (vinyl chloride)—PVC |
| vinyl acetate | manufacture of poly (vinyl acetate) used in paint emulsions, plywood adhesives and textiles |
| polyethylene | “plastic” bags; toys; packaging |
Produced from propylene (propene)
| Chemical | Uses |
|---|---|
| isopropyl alcohol | rubbing alcohol; cosmetics; synthesis of acetone |
| propylene oxide | manufacture of polyurethanes; polyesters |
| cumene | industrial preparation of phenol and acetone |
| polypropylene | molded articles (e.g., kitchenware); fibres for indoor-outdoor carpeting |
Industrial Preparation of Ethylene and Propylene
Ethene (CH 2 CH 2 ) and propene (CH 3 CHCH 2 ), are most often called by their common names—ethylene and propylene. Ethylene is a major commercial chemical. The US chemical industry produces about 25 billion kilograms of ethylene annually, more than any other synthetic organic chemical. More than half of this ethylene goes into the manufacture of polyethylene, one of the most familiar plastics. Propylene is also an important industrial chemical. It is converted to plastics, isopropyl alcohol, and a variety of other products. Both ethylene and propylene are the feedstock for the industrial synthesis of a wide variety of small organic molecules.
Ethylene, propylene, and butylene (CH 3 CH 2 CHCH 2 ) are typically industrially synthesized through the steam cracking of light alkanes (C < 8) obtained from fractional distillation of crude oil. Cracking is the name given to a number of petroleum refining processes which break up large hydrocarbon molecules into smaller fragment. Steam cracking is achieved without a catalyst by using high temperatures (~900 o C) and produces a mixtures of products containing high proportions of hydrocarbons with double bonds. There is not any single unique reaction happening during steam cracking. The hydrocarbon molecules are broken up in a fairly random way but the process can be generically represented by the reaction below.
The mechanism of the steam cracking is complex and believed to involve the formation of free radicals. The high temperatures of steam cracking is enough to cause the homolytic cleavage of C-C and C-H bonds in the starting material. The cleavage of C-C bonds inherently creates smaller hydrocarbons as represented below.
Industrial Preparations of Alcohols from Ethylene and Propylene
Ethanol is manufactured by reacting ethylene with steam. The catalyst used is solid silicon dioxide coated with phosphoric acid. The reaction is reversible.
Only 5% of the ethylene is converted into ethanol at each pass through the reactor. By removing the ethanol from the equilibrium mixture and recycling the ethylene, it is possible to achieve an overall 95% conversion.
Isopropyl alcohol is synthesized on an industrial scale using a similar reaction with propylene.
Ethylene is also used in the industrial synthesis of ethylene glycol. Ethylene glycol is a major industrial compound with a wide range of applications. The traditional method to synthesize ethylene glycol is a two step process in which ethylene is directly oxidized to ethylene oxide. Next the three-membered ring of ethylene oxide is opened using water at high temperatures and pressures to form ethylene glycol.
Industrial Preparations of Plastics from Ethylene and Propylene
One of the primary uses of industrial synthesized ethylene is the production of the polymer polyethylene (PE) . Polyethylene is the most common plastic. As of 2017, over 100 million tons of polyethylene resins are produced annually, accounting for 34% of the total plastics market. Its primary use is in packaging (plastic bags, plastic films, geomembranes, containers including bottles, etc.). Many kinds of polyethylene are known, with most having the chemical formula (C 2 H 4 ) n .
It is the simplest polymer, consisting of random-length (but generally very long) chains made up of two-carbon units. During the polymerization process many ethylene molecules are linked together to form the carbon backbone of polyethylene. In the polyethylene structures are represented below. The squiggly lines at the ends of the long structure indicate that the same pattern extends indefinitely. The more compact notation on the right shows the minimal repeating unit enclosed in brackets; this means the same thing and is the preferred way of depicting polymer structures.


1.5: Putting It Together- Communicating in Business
We’ve learned that there are seven principles by which you should evaluate any communication, be it verbal or written:
- Clear
- Concise
- Objective
- Consistent
- Complete
- Relevant
- Understanding of Audience Knowledge
If you adhere to these principles, you have a far better chance of being understood by your audience.
We’ve also learned about the social communication model. Through that, we learned that you create the message in your head and “encode it” into a message that can be understood, and then your audience “decodes” it to receive the message. In that process, there can be disruptive “noise” that distorts your message, but your audience can provide “feedback” that allows you additional chances to be understood.
We learned that there are types of communication—written, yes, but also spoken. And with spoken communication, verbal, listening and non-verbal communication are all taking place at the same time.
Finally, we considered ethical communication and how keeping these principles and laws of communication in mind can keep you on the straight and narrow path to ethical communication.
You’re on your way to being a great communicator!
Contributors and Attributions
- Putting It Together: Communicating in Business. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution


19.2E: Lymph Trunks and Ducts
The lymph trunks drain into the lymph ducts, which in turn return lymph to the blood by emptying into the respective subclavian veins.
- Describe the types of lymph vessels and lymph trunks and their roles
Key Points
- The lymph trunks drain into the lymph ducts, which in turn return lymph to the blood by emptying into the respective subclavian veins.
- There are two lymph ducts in the body: the right lymph duct and the thoracic duct.
- There are four pairs of lymph trunks: jugular lymph trunks, subclavian lymph trunks, bronchomediastinal lymph trunks, and lumbar lymph trunks. In addition, the intestinal lymph trunk is unpaired.
- The intestinal lymph trunk and the thoracic lymph duct contain chyle, a mixture of emulsified fats from the intestines and lymph fluid.
Key Terms
- thoracic duct : The lymph duct that drains lymph and chyle from the lower and left halves of the body.
- subclavian vein : Two large veins, one on either side of the body, with a diameter similar to that of the smallest finger.
- lymph : A colorless, watery body fluid carried by the lymphatic system, consisting mainly of white blood cells.
After filtration by the lymph nodes, efferent lymphatic vessels take lymph to the end of the lymphatic system. The final goal of the lymphatic system is to recirculate lymph back into the plasma of the bloodstream. There are two specialized lymphatic structures at the end of the lymphatic system, called the lymph trunks and ducts.
Lymphatic Trunks
Lymphatic Ducts : The thoracic duct and right lymphatic duct.
A lymphatic trunk is any large lymph vessel that forms from the convergence of many efferent lymph vessels. There are four sets of of lymph trunks that are paired with a right and left half, and one unpaired trunk:
- Jugular lymph trunks, located in the neck, drain lymph fluid from the cervical lymph nodes of the neck.
- Subclavian lymph trunks, located beneath the clavicle, drain lymph fluid from the apical lymph nodes around the armpit, which carry lymph from the arms.
- Bronchomediastinal lymph trunks, located in the chest, drain lymph fluid from the lungs, heart, trachea, mediastinal, and mammary glands.
- Lumbar lymph trunks are the lower pair of lymph trunks that drain lymph fluid from the legs, pelvic region, and kidneys.
- Intestinal lymph trunk is the unpaired lymph trunk that receives chyle (lymph mixed with fats) from the intestines. Chyle typically has a high fatty acid content.
Lymphatic trunks then drain lymph fluid into the lymph ducts, the final part of the lymphatic system.
Lymph Ducts
Two lymph ducts receive lymph from the lymph trunks. These are the largest lymph vessels and contain three layers, similar to those of great veins.
- The thoracic lymph duct, the largest lymph vessel in the body, takes lymph from the lower and left halves of the body. Because the thoracic lymph duct drains the intestinal lymph trunks, it carries a mixture of lymph and emulsified fatty acids called chyle back to the bloodstream.
- The right lymphatic duct receives lymph from the right and upper halves of the body, including the right sides of the jugular, bronchomediastinal, and subclavian lymph trunks.
The thoracic duct drains into to the left subclavian vein while the right duct drains into the right subclavian vein, both at the junction between the respective vein and the jugular vein. The two subclavian veins then merge into the vena cava, the large vein that brings deoxygenated blood to the heart. The lymph ducts each have internal valves at their junction with the subclavian vein. These function similarly to other lymphatic valves and prevent venous blood from flowing into the lymph duct. This point marks the end of lymph fluid’s journey through the lymphatic system.
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- Curation and Revision. Authored by : Boundless.com. Provided by : Boundless.com. License : CC BY-SA: Attribution-ShareAlike
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- Lymphatic vessels. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Lymphat..._of_Lymphatics . License : CC BY-SA: Attribution-ShareAlike
- endothelial cells. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/endothelial%20cells . License : CC BY-SA: Attribution-ShareAlike
- ISF. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/ISF . License : CC BY-SA: Attribution-ShareAlike
- adventitia. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/adventitia . License : CC BY-SA: Attribution-ShareAlike
- Lymphatic vessel. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Lymphatic_vessel . License : CC BY-SA: Attribution-ShareAlike
- Lymph flow. Provided by : Wikimedia. Located at : upload.wikimedia.org/wikipedi...mph_vessel.png . License : Public Domain: No Known Copyright
- Lymphatic system. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Lymphatic_system . License : CC BY-SA: Attribution-ShareAlike
- lymph. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/lymph . License : CC BY-SA: Attribution-ShareAlike
- plasma. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/plasma . License : CC BY-SA: Attribution-ShareAlike
- Lymph flow. Provided by : Wikimedia. Located at : upload.wikimedia.org/wikipedi...mph_vessel.png . License : Public Domain: No Known Copyright
- Illu lymphatic system. Provided by : Wikimedia. Located at : commons.wikimedia.org/wiki/Fi...tic_system.jpg . License : Public Domain: No Known Copyright
- Lymphatic nodules. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Lymphat...ic_circulation . License : CC BY-SA: Attribution-ShareAlike
- lymph. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/lymph . License : CC BY-SA: Attribution-ShareAlike
- afferent lymphatic vessels. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/afferen...atic%20vessels . License : CC BY-SA: Attribution-ShareAlike
- subcapsular sinus. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/subcapsular%20sinus . License : CC BY-SA: Attribution-ShareAlike
- Lymph flow. Provided by : Wikimedia. Located at : upload.wikimedia.org/wikipedi...mph_vessel.png . License : Public Domain: No Known Copyright
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- Lymphatic capillaries. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Lymphatic_capillaries . License : CC BY-SA: Attribution-ShareAlike
- lymph capillaries. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/lymph%20capillaries . License : CC BY-SA: Attribution-ShareAlike
- interstitial fluid. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/interstitial_fluid . License : CC BY-SA: Attribution-ShareAlike
- Lymph flow. Provided by : Wikimedia. Located at : upload.wikimedia.org/wikipedi...mph_vessel.png . License : Public Domain: No Known Copyright
- Illu lymphatic system. Provided by : Wikimedia. Located at : commons.wikimedia.org/wiki/Fi...tic_system.jpg . License : Public Domain: No Known Copyright
- Schematic_of_lymph_node_showing_lymph_sinuses.svg. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Lymph_...ph_sinuses.svg . License : CC BY-SA: Attribution-ShareAlike
- Illu lymph capillary. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Il..._capillary.png . License : Public Domain: No Known Copyright
- Lymph duct. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Lymph_duct . License : CC BY-SA: Attribution-ShareAlike
- Lymph vessel. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Lymph_vessel . License : CC BY-SA: Attribution-ShareAlike
- Lymph trunk. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Lymph_trunk . License : CC BY-SA: Attribution-ShareAlike
- lymph. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/lymph . License : CC BY-SA: Attribution-ShareAlike
- subclavian vein. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/subclavian%20vein . License : CC BY-SA: Attribution-ShareAlike
- thoracic duct. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/thoracic%20duct . License : CC BY-SA: Attribution-ShareAlike
- Lymph flow. Provided by : Wikimedia. Located at : upload.wikimedia.org/Wikipedia/commons/0/00/Lymph_vessel.png . License : Public Domain: No Known Copyright
- Illu lymphatic system. Provided by : Wikimedia. Located at : commons.wikimedia.org/wiki/Fi...tic_system.jpg . License : Public Domain: No Known Copyright
- Schematic_of_lymph_node_showing_lymph_sinuses.svg. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Lymph_...ph_sinuses.svg . License : CC BY-SA: Attribution-ShareAlike
- Illu lymph capillary. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Il..._capillary.png . License : Public Domain: No Known Copyright
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9: Cell Communication
While the necessity for cellular communication in larger organisms seems obvious, even single-celled organisms communicate with each other. Yeast cells signal each other to aid mating. Some forms of bacteria coordinate their actions in order to form large complexes called biofilms or to organize the production of toxins to remove competing organisms. The ability of cells to communicate through chemical signals originated in single cells and was essential for the evolution of multicellular organisms. The efficient and error-free function of communication systems is vital for all life as we know it.
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- 9.1: Signaling Molecules and Cellular Receptors
- Chemical signals are released by signaling cells in the form of small, usually volatile or soluble molecules called ligands. A ligand is a molecule that binds another specific molecule, in some cases, delivering a signal in the process. Ligands can thus be thought of as signaling molecules. Ligands interact with proteins in target cells, which are cells that are affected by chemical signals; these proteins are also called receptors.
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- 9.2: Propagation of the Signal
- Once a ligand binds to a receptor, the signal is transmitted through the membrane and into the cytoplasm. Continuation of a signal in this manner is called signal transduction. Signal transduction only occurs with cell-surface receptors because internal receptors are able to interact directly with DNA in the nucleus to initiate protein synthesis. When a ligand binds to its receptor, conformational changes occur that affect the receptor’s intracellular domain.
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- 9.3: Response to the Signal
- Inside the cell, ligands bind to their internal receptors, allowing them to directly affect the cell’s DNA and protein-producing machinery. Using signal transduction pathways, receptors in the plasma membrane produce a variety of effects on the cell. The results of signaling pathways are extremely varied and depend on the type of cell involved as well as the external and internal conditions. A small sampling of responses is described below.


3.6: Beginning to Evaluate Arguments
Before I said that we use argument mapping to understand an argument before we do any evaluation of those arguments as good or bad arguments, valid or invalid, cogent or uncogent, sound or unsound, and so on.
But the process of identifying hidden assumptions is in itself a sort of evaluative process: we must identify the need in the argument for another claim to be true—we have to declare that an argument is incomplete and therefore faulty before we can talk about the argument needing an extra premise.
So if we’ve already done a bit of evaluating of arguments in identifying hidden premises, perhaps those tools that we gained when we were identifying hidden assumptions will help us in trying to evaluate an argument as a good or bad argument. Let’s explore how helpful those tools are.
Recall that the central idea in the process of identifying hidden assumptions is the idea that a good, complete argument has a series of topics or terms that are linked together in the right way. This is a really informal and incomplete version of what you might learn if you learn Categorical or Aristotelian Logic. That’s the study of how categories or terms must be linked for an argument to be deductively valid.
Let’s look at how this informal idea can help us determine whether we’ve got a good or bad argument. Here’s an example to consider—it’s something you might see on social media and in the wording that one might actually find there:
If you don’t want an abortion, don’t have one.
[Implied conclusion: Abortion should remain legal and available].
Hopefully it’s relatively clear that this argument needs a tune up—not because it is wrong-headed (it might not be) or because its conclusion is wrong (it might be true), but because it’s unclear what the actual argument is: what are the premises and how do they support the conclusion?
First, we should try to interpret the argument in a way that makes the process of identifying topics easier. This process is already a bit evaluative in that we are interpreting the argument charitably: we’re trying to understand the most rational version of the argument without changing its essential content. Maybe something like:
Abortion rights aren’t abortion mandates,
so there’s no reason to oppose abortion rights.
Making abortion legal doesn’t mean requiring (mandating) anyone to have an abortion. This is already starting to look more complete, and it’s already beginning to look like a serious philosophical argument. We’ve taken it out of the format of a slogan and interpreted it as an argument.
The next step is to identify the topics being discussed:
a. Abortion rights laws
b. Abortion mandates
c. Reason to oppose things
Once we’ve identified these terms, we can think about the argument in terms of a series of propositions which connect them together.
1. Abortion Rights laws aren’t abortion mandates
[Links (a) to (b)]
2. So, There’s no reason to oppose abortion rights
[Links (c) to (a)]
We’ve got some of the tools now to recognize that there’s a missing premise here. Can you find it?
Ummm....There’s no link between Reason to oppose things and Abortion mandates, so the inference has a gap in it.
Right-o! Good work. We’ve linked a to b, and a to c, but not b to c. This is why the argument feels a bit gappy and incomplete. What, then, might our hidden premise be? We need to link “Abortion mandates” with “reason to oppose things.” Any ideas?
Yeah. Why not something like “There’s no reason to oppose abortion mandates.”
Well...not quite. That’s a pretty clearly false, statement right? Lots of people want to have children and lots of other people are morally opposed to abortions, so it makes little sense to say there’s no reason to oppose mandating everyone has an abortion, right?
Oh...yeah. What about “If something isn’t a mandate, then there’s no reason to oppose it.”
Now we’re talking! That’s a really general claim: it applies to everything (or at least every public policy or law) that isn’t a mandate. So maybe we’d want something more restrictive. Nevertheless, this is a good start. So here’s our complete argument:
1. Abortion rights laws aren’t abortion mandates
[Links (a) to (b)]
1a. If something isn’t a mandate, then there’s no reason to oppose it
[Links (b) to (c)]
2. So, There’s no reason to oppose abortion rights laws
[Links (c) to (a)]
This process is tricky and interpretive. When we get to Aristotelian Logic, we’ll cover some tools that make this a more strict and formalized process. For now, though, we’re sticking with intuitively understanding arguments and how they hang together. This is an incredibly valuable skill in all aspects of life: when is an inference making an implicit assumption? People make loads of implicit assumptions all of the time.
Okay, so the goal in this section was to start to evaluate arguments using some of the tools we’ve picked up so far. Here’s how this might go:
The first claim in this argument is that Abortion rights aren’t abortion mandates . This is clearly true. No law or policy securing abortion rights (within the realm of reasonable laws) would require that people have abortions. So there’s no problem with the first claim.
The second (hidden) claim in the argument is that If something isn’t a mandate, then there’s no reason to oppose it. This, as I said before, is very broad. It seems easy to come up with a counterexample. In this case, a counterexample would be something that isn’t a mandate, but which we would have reason to oppose. Can you think of a possible law that doesn’t put a requirement on citizens, but nevertheless is a law we’d want to oppose?
I can think of thousands. A law allowing murder. A law allowing ritual human sacrifice. A piece of legislation requesting that the President strongly consider nuking the moon....the list goes on.
So this seems like a bad principle: one shouldn’t be opposed to something that doesn’t bring a mandate with it. In other words: if it doesn’t interfere with you, then leave it alone. That’s not how a civil society, works though. We take an interest in each other’s lives for the sake of having a healthy society and protecting one another.
As I said a few paragraphs back: this hidden premise we inserted completes the argument fairly directly, but might be too general . More general than we need, in fact. We might consider something more specific like “If a law doesn’t require people to do something immoral, then there’s no reason to oppose it.” But that is refuted by the same counterexamples I listed above. We could try over and over to find more specific premises to complete the argument, but honestly at some point we have to admit that the argument as we’ve reconstructed it probably rests on a false general premise.
So in reconstructing this argument and identifying what hidden premise it rests on, we have set ourselves up to evaluate whether or not this is a good argument. You might disagree, but this seems like a bad argument for abortion rights. Best to go looking elsewhere for good arguments for abortion rights (they’re out there! Philosophers like Judith Jarvis Thomson, Mary Anne Warren, and Rosalind Hursthouse have interesting arguments indeed).


12.1: Sleep and Rest Introduction
- Assess factors that put patients at risk for problems with sleep
- Identify factors related to sleep/rest across the life span
- Recognize characteristics of sleep deprivation
- Consider the use of nonpharmacological measures to promote sleep and rest
- Identify evidence-based practices
Maslow’s hierarchy of needs indicates sleep as one of our physiological requirements. Getting enough quality sleep at the right times according to our circadian rhythms can protect mental and physical health, safety, and quality of life. Conversely, chronic sleep deficiency increases the risk of heart disease, kidney disease, high blood pressure, diabetes, and stroke, as well as weakening the immune system. [1] This chapter will review the physiology of sleep and common sleep disorders, as well as interventions to promote good sleep.
- Trossman, S. (2018, November 7). Nurses offer strategies to promote patients’ rest and sleep. American Nurse . https://www.myamericannurse.com/strategies-promote-patients-rest-sleep/ ↵


1.8: The Future of Communication
Students and scholars of communication now ask the question: What will the future hold for communication studies, and what will the next big revolution bring? That question has yet to be answered, though many theories exist. Perhaps the next leap forward will occur in the communication of emotion, as the limbic brain (or part of the brain responsible for the way humans feel) has no capacity for language. Will future technology allow people to sense and translate emotions from person to person, allowing humanity to empathize with one another more efficiently? Perhaps the next big advance will resemble telepathy, allowing individuals to transmit thought without the need for language. Today, however, verbal communication, whether vocally through the act of speaking or in writing, remains the primary means of sharing information.
Regardless of what the future may hold, everyone now lives in an exciting time of flux and dynamic change. People now have vast oceans of information at their fingertips, and though this provides them with a myriad of possibilities, the potential for disaster coexists. To navigate the seas of information overload, individuals must take a step back and observe such changes from a more mindful, objective perspective, rather than allowing themselves to get caught up like rats in a psychology experiment (see B. F. Skinner ), mindlessly clicking away on links generated by an algorithm that knows their deepest secrets. As with the alphabet, the printing press, and the Industrial Revolution, humanity will eventually grow accustomed to this change in due process, but only if it charts a careful, rational course. Winners and losers will emerge from the dust as it settles, and those with the impetus for the study of the complexities of human communication will most likely remain unscathed.
Activity
Visit www.google.com/images , type “communication model” into the search field, and then hit enter. Scroll through a few pages’ worth of images and take note of the staggering number of diverse visual depictions of communication. Why do you think are there so many ways of explaining the same “basic” concept?