Deriving (Literally) the Velocity of the Center of Mass


Starting with the center-of-mass equation:

x_cm

take the derivative of both sides (with respect to time, t), while keeping in mind that the masses are constant:

d(x_cm)/dt =

Now, all of the d(x)/dt's, (the rate the position changes), are velocties, v. Therefore:

vcm =

which is the desired result.


last update February 5, 2010 by JL Stanbrough