Question

What is the relation between angular velocity, tangential velocity and position vector

Answer 1

Technically speaking, as tangential velocity is a vector, then it cannot be constant for any object with a non-zero angular velocity. That’s because the latter implies a change of direction and hence a change in tangential velocity.

However, if the question is whether the angular velocity and magnitude of tangential velocity can both be constant, then the answer is yes. Any object undergoing uniform circular motion around a fixed point will have both a constant angular velocity and a constant magnitude of tangential velocity.

Further, if the object undergoes a constant angular acceleration on a circular path around a fixed point, then the magnitude of the tangential acceleration will also be constant.