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 increases to 40 rad/s. Assume that the angular acceleration was constant during the 5.0-s interval. How many revolutions does the wheel turn through during the 5.0-s interval?
A) 20 rev
B) 24 rev
C) 32 rev
D) 28 rev
E) 39 rev

Question

Quizplus · Accepted Answer

The total number of revolutions can be found using the formula for angular displacement $\theta = \omega_0 t + \frac{1}{2} \alpha t^2$, where $\omega_0$ is the initial angular velocity, $\alpha$ is the angular acceleration, and $t$ is the time. First, find the angular acceleration $\alpha = \frac{\Delta \omega}{\Delta t} = \frac{40 \text{ rad/s} - 20 \text{ rad/s}}{5.0 \text{ s}} = 4 \text{ rad/s}^2$. Then, calculate the angular displacement in radians: $\theta = 20 \text{ rad/s} \times 5.0 \text{ s} + \frac{1}{2} \times 4 \text{ rad/s}^2 \times (5.0 \text{ s})^2 = 100 + 50 = 150 \text{ rad}$. Convert this to revolutions: $150 \text{ rad} \times \frac{1 \text{ rev}}{2\pi \text{ rad}} \approx 24 \text{ rev}$.

A Wheel Rotates About a Fixed Axis with an Initial