A ball is whirled in a circle by attaching it to a fixed point with a string. Is there an angular rotation of the ball about its center? If yes, is this angular velocity equal to the angular velocity of the ball about the fixed point?
Yes, the ball is going to have an angular rotation about its center.
The angular velocities are going to be same. When the conjunction of ball and string reaches the initial point, the ball reaches the same point too. Hence, they are moving with same angular velocities. So, the angular velocity about the center is equal to the angular velocity of the ball about the fixed point.