An amusement park merry-go-round at its constant operational speed makes one complete rotation in \(45 \mathrm{~s}\). Two children are on horses, one at \(3.0 \mathrm{~m}\) from the center of the ride and the other farther out, \(6.0 \mathrm{~m}\) from the center. What are

(a) the angular speed and

(b) the tangential speed of each child?

THINKING IT THROUGH. The angular speed of each child is constant and the same, since both children make a complete rotation in the same time. However, the tangential speeds will be different, because the radii are different. That is, the child at the greater radius travels in a larger circle during the rotation time and thus must travel faster.