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[Phys-L] center of mass etc.



On 12/01/2016 08:46 AM, Philip Keller wrote:
one of my
students pointed out that the center-of-mass velocity is the average of the
initial and final velocity of either object. Good point...

Here's another average, also useful: At any given time, the
CM velocity is the weighted average of the objects' velocities.
For dissimilar objects, it has to be the /weighted/ average.

Σ m V
Vcm = -------- [1]
Σ m

One might conjecture that this is where the term "weighted" average
originated. In statistics in general, averages can be weighted
by all sorts of abstract weighting factors ... but in the case of
the CM velocity, the weighting factor for each object is literally
its mass.

Equation [1] generalizes to N objects, for all N from 1 on up,
even for dissimilar objects.

It also generalizes to any dimensionality, from 1D on up.