Question

A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving?A) 5.64 m/s B) 3.50 m/s C) 0.556 m/s D) 1.75 m/s E) 1.80 m/s

Answer 1

B) 3.50 m/s

Step-by-step explanation:

The linear velocity in a circular motion is defined as:

`v=\omega r(1)`

The angular frequency (
`\omega`) is defined as 2π times the frequency and r is the radius, that is, the distance from the center of the circular motion.

`\omega=2\pi f(2)`

Replacing (2) in (1):

`v=2\pi fr`

We have to convert the frequency to Hz:

`7.18rpm*(1Hz)/(60rpm)=0.12Hz`

Finally, we calculate how fast is the child moving:

`v=2\pi(0.12Hz)(4.65m)\\v=3.5(m)/(s)`