Collisions and the Center of Mass

To gain some intuition about the location of the CM, let’s add the term ( )m r m r2 1 2 1 0 I I− = to the numerator of

this equation, leaving it unchanged while allowing us to re-group terms usefully:

I I I I I I I I R

m r m r m r m r m m

m m r m r r CM =

+ + −( ) + =

r m m m

r r

+

= + + −( ) I I I .