Question

If no external force is acting on a two body system, what will happen to (a) velocity of centre of mass (b) angular momentum?

Answer 1

If no external force is acting on two body system then effect on velocity of centre of mass is velocity remains constant and effect on angular momentum is it also remains constant.

(a) In absence of any external force, the center of mass of a two body system will have zero acceleration.

Since, F = m$a_{cm}$

=> 0 = m$a_{cm}$

=> = 0

where is the acceleration of the centre of mass

So, the center of mass of the system will continue its state of rest or of uniform motion. i.e velocity will remain constant as acceleration is defined as rate of change of velocity and here acceleration is zero.

(b) Angular momentum = mvr  

Since velocity is constant , angular momentum will also remain constant.