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) 3.50 m/s
B) 1.75 m/s
C) 1.80 m/s
D) 0.556 m/s
E) 5.64 m/s

Question

Quizplus · Accepted Answer

The speed of the child can be calculated using the formula for linear velocity, $v = r\omega$, where $v$ is the linear velocity, $r$ is the radius (distance from the center), and $\omega$ is the angular velocity in radians per second. First, convert the angular velocity from revolutions per minute (rpm) to radians per second: $7.18 \, \text{rpm} = 7.18 \times \frac{2\pi}{60} \, \text{rad/s}$. Then, calculate the linear velocity: $v = 4.65 \times 7.18 \times \frac{2\pi}{60} \approx 3.50 \, \text{m/s}$.

A Child Is Riding a Merry-Go-Round That Is Turning at 7.18