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

Answer:

B) 3.50 m/s

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:

$7.18rpm*\frac{1Hz}{60rpm}=0.12Hz$

Finally, we calculate how fast is the child moving:

$v=2\pi(0.12Hz)(4.65m)\\v=3.5\frac{m}{s}$