Rigid body dynamics r and velocities v. Select a reference point R and compute the relative position and velocity vectors, The total linear and angular momentum vectors relative to the reference point R are and If R is chosen as the center of mass these equations simplify to To specialize these formulas to a rigid body, assume the particles are rigidly connected to each other so P, i=1...,n are located by the coordinates r and velocities v. Select a reference point R and compute the relative position and velocity vectors, where ω is the angular velocity of the system. The linear momentum and
Escape velocity kg or 1,000 kg; what differs is the amount of energy required. For an object of mass formula_9 the energy required to escape the Earth's gravitational field is "GMm / r", a function of the object's mass (where "r" is the radius of the Earth, "G" is the gravitational constant, and "M" is the mass of the Earth, ). A related quantity is the specific orbital energy which is essentially the sum of the kinetic and potential energy divided by the mass. An object has reached escape velocity when the specific orbital energy is greater or equal to zero. An