A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval?
A) 95 rad
B) 85 rad
C) 65 rad
D) 75 rad
E) 125 rad

Question

Quizplus · Accepted Answer

The wheel turns through 75 radians. This can be calculated using the formula for angular displacement $\theta = \omega_0 t + \frac{1}{2} \alpha t^2$, where $\omega_0$ is the initial angular velocity, $t$ is the time, and $\alpha$ is the angular acceleration. First, find the angular acceleration using $\alpha = \frac{\Delta \omega}{\Delta t} = \frac{10 \, \text{rad/s} - 20 \, \text{rad/s}}{5.0 \, \text{s}} = -2 \, \text{rad/s}^2$. Then, calculate the angular displacement: $\theta = 20 \, \text{rad/s} \times 5.0 \, \text{s} + \frac{1}{2} \times (-2 \, \text{rad/s}^2) \times (5.0 \, \text{s})^2 = 100 \, \text{rad} - 25 \, \text{rad} = 75 \, \text{rad}$.

A Wheel Rotates About a Fixed Axis with an Initial