@JohnRennie, in a rigid body the distance between any two points does not decrease right. So at any instant $\vec v_P \cdot (\vec r_P - \vec r_Q)= \vec v_Q \cdot (\vec r_P - \vec r_Q)$ for any two points but why does differentiating this equation not work. Why can the acceleration along the line joining two points be unequal?

ps - an example would be centripetal acceleration, with points being on the same normal to the axis of rotation. I intuitively feel the accelerations should be equal or the body would get squished up...