Classical mechanics

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Classical mechanics refers to a branch of physics dealing with every-day laws of mechanics (as opposed to quantum mechanics). The term is sometimes interchangeable with "Newtonian physics", as it was Sir Isaac Newton who first proposed the first laws of motion. However, there are other formulations of classical mechanics that are not due to Newton, namely Lagrangian dynamics and Hamiltonian dynamics. (These are simply different formulations of the same principles; they are precisely equivalent to Newtonian mechanics.) Classical mechanics is sufficient for explaining most observable phenomena.














2. In an inertial reference frame, the net force acting upon an object is equal to the rate of change of its momentum. Mathematically:


is the net force acting on the object
is the momentum of the object

Momentum is defined as the product of mass and velocity, . If the mass of the object in question is constant, then substituting if for the momentum we find Newton's second law may be rewritten in the more familiar form of:


is the mass of the object
is the acceleration of the object

This law also applies to a system of objects.



If object A exerts a force on object B, object B will exert a force equal in magnitude and opposite in direction on object A. For example, if the earth pulls you down with a force of 1500 Newtons, you pull up on the earth with a force of 1500 Newtons. (Of course, since , and the earth's mass is much greater than yours, the earth accelerates much less than you do.)

Angular Kinematics



Classical mechanics breaks down in extreme conditions, such as traveling close to the speed of light, being near extremely high gravity or dealing with very small distances as are important when dealing with subatomic particles.


Relativity deals with objects traveling near the speed of light or near extremely strong gravitational fields, such as black holes.

In special relativity, the Lorentz factor, , can be used to judge whether the difference between classical mechanics and relativity is significant. A value close to 1 indicates that relativistic effects are negligible.


is the velocity of an object
is the speed of light

Speeds necessary to get a significant Lorentz factor are simply not found in real-life examples of visible objects. For example, at 5 miles per second, (18,000 miles per hour, the speed of a satellite in Earth orbit), the Lorentz factor has a value of 1.000000000360219.

Quantum Mechanics

Quantum mechanics describes the behaviour of matter at small distances, such as those of atoms or subatomic particles. Given enough information about a classical system, we can use classical mechanics to predict how it will evolve with certainty. This is not true in quantum mechanics; in quantum mechanics, we can only calculate the probability of say the measurement of the position of a particle. This results from the wave-like nature of matter, referred to as wave-particle duality. It states that particles (such as electrons) can sometimes behave like waves and waves (such as light) can sometimes behave like particles. The reason we don't observe quantum effects on macroscopic scales can be seen by considering the equation for the wavelength, of a particle:

where is Planck's constant and is the momentum (physics) of the particle. At macroscopic scales, is very small as Planck's constant is such a small number, . Therefore, the wave-like nature of matter has little effect on macroscopic scales.

The wave-like nature of matter leads to the Heisenberg uncertainty principle, which states that there are certain quantities, such as position and momentum, that cannot be measured to an arbitrary precision simultaneously.

Particles are described by a wavefunction, , which encodes the results of all possible measurements. The wavefunction is the solution to the Schrodinger equation,

where is the reduced Planck's constant, is the mass of the particle and is the potential the particle is in.