Once the ball is going quickly and we don't hit it again, we can treat the angular speed as being isolated.target $1$ of $5$

We can treat the ball as a point mass at the end of the rope and write equation for the angular momentum of the ball: L$=$mr$2$L$=$mr$2$$.$target $2$ of $5$

The angular momentum of the system is constant, so angular speed must increase as radius rr decreases, and increasing Blank means a shorter period.