Fastest direction in circular trajectory

Question

I have a point P and a vector V. This point is describing a uniform circular trajectory with linear velocity lv and angular velocity av. This trajectory passes through a point P', how do I find out if I would reach P' faster if I went backwards (-V) instead of forward?

Answer 1

Could you be more precise what you mean by linear velocity and angular velocity? If I get your question right, you have to check whether the inner product $\langle P'-P,V \rangle$ is positive. If this is the case, you move in the "right" direction with $V$ and reach $P'$ faster with $V$ than with $-V$.