Express the angular speed in radians per second.
-A carousel has a radius of 18 feet and takes 31 seconds to make one complete revolution. What is the linear speed of the carousel at its outside edge? Express the answer in feet per second. If necessary, round the answer to two decimal places.
A) $3.65$ feet per second
B) $0.58$ feet per second
C) $10.82$ feet per second
D) $113.1$ feet per second

Question

Quizplus · Accepted Answer

The linear speed $v$ of the carousel at its outside edge can be found using the formula $v = \omega r$, where $\omega$ is the angular speed in radians per second and $r$ is the radius. Since the carousel makes one complete revolution (which is $2\pi$ radians) in 31 seconds, its angular speed $\omega = \frac{2\pi}{31}$ radians per second. Therefore, the linear speed $v = \frac{2\pi}{31} \times 18 \approx 3.65$ feet per second.

Express the Angular Speed in Radians Per Second 3.653.653.65 Feet Per Second B)

Express the Angular Speed in Radians Per Second $3.65$ Feet Per Second
B)