A5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. it slows down and stops in 20 s. what is the angular acceleration as it stops.

First, we can find the initial angular speed of the merry-go-round. Calling the period of revolution, the initial angular speed is


Then, the merry-go-round starts to decelerate, so it is an angular accelerated motion with angular acceleration , and the angular velocity follows the law

We know that after t=20 s, the merry go round stops, so . So we can rewrite the previous equation and solve it to find :


where the negative sign means the merry-go-round is decelerating.