A golfer swings a golf club, making a long drive from the tee. Do all points on the ciub have the same angular veiocity at any instant while the club is in motion?

Yes, all the points on the club have the same angular velocity at any instant while the club is in motion. A point located far off from the axis of rotation has larger velocity relative to a point located nearby, therefore the ratio of the magnitude of velocity of the point to that with their distance from the axis of rotation remains constant.This ratio is magnitude of the angular velocity.