Question

A 5.0-m-diameter merry-go-round is initially turning with a 3.9s period. What is the speed of a child on the rim?

Answer 1

If there is a period of motion, then motion is uniform. In this case, this is circular motion.
You can rewrite the velocity as a function of the period. Basically, consider a circle's circumference and how long it takes to go around it. That would be the period.

\[v = \frac{circumference}{period}=\frac{2 \pi r}{\tau}\]
In this case, 'r' is the radius, which is half of the diameter. 'tau' is the period, which is given.