Evaluate the following two statements: (A) The linear momentum of...

The linear momentum of a system is given by $\vec{P} = M\vec{v}_{cm}$, where $M$ is the total mass and $\vec{v}_{cm}$ is the velocity of the centre of mass.

If the centre of mass is at rest (Statement B), then $\vec{v}_{cm} = 0$. This gives $\vec{P} = 0$, which is a constant. Thus, B implies A.

If the linear momentum of the system is constant (Statement A), then $\vec{v}_{cm}$ is a constant vector. This constant velocity can be non-zero, meaning the centre of mass may not be at rest. Thus, A does not imply B.

Therefore, B implies A but A does not imply B.