Question

on a ferris wheel, sarah observes that it takes 45 seconds for her chair to complete a full revolution. her chair is 30 feet from the axle of the ferris wheel. to the nearest hundredth, sarahs angular velocity is radians per minute.

Explanation:

Step1: Recall angular - velocity formula

The formula for angular velocity $\omega$ is $\omega=\frac{\theta}{t}$, where $\theta$ is the angle of rotation and $t$ is the time. For a full - revolution, $\theta = 2\pi$ radians. The time for a full - revolution is $t = 45$ seconds. First, find the angular velocity in radians per second.
$\omega_{s}=\frac{2\pi}{45}$ radians per second.

Step2: Convert seconds to minutes

Since we want the angular velocity in radians per minute, and there are 60 seconds in a minute. We use the conversion factor. Multiply the angular velocity in radians per second by 60.
$\omega=\frac{2\pi}{45}\times60=\frac{2\pi\times60}{45}=\frac{120\pi}{45}=\frac{8\pi}{3}\approx8.38$ radians per minute.

Answer:

$8.38$