A wheel initially has an angular velocity of 18 rad/s but it is slowing at a rate of 2.0 rad/s².By the time it stops it will have turned through: A)81 rad B)160 rad C)245 rad D)330 rad E)410 rad

Question

Quizplus · Accepted Answer

The wheel stops when its angular velocity reaches 0 rad/s. Using the equation 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. Since the wheel is slowing down, $\alpha = -2.0 \, \text{rad/s}^2$, and we need to find $t$ when $\omega = 0$. Using $\omega = \omega_0 + \alpha t$, we get $0 = 18 - 2t$, so $t = 9 \, \text{s}$. Substituting $t = 9 \, \text{s}$, $\omega_0 = 18 \, \text{rad/s}$, and $\alpha = -2.0 \, \text{rad/s}^2$ into the displacement equation gives $\theta = 18(9) + \frac{1}{2}(-2)(9)^2 = 162 - 81 = 81 \, \text{rad}$.

A Wheel Initially Has an Angular Velocity of 18 Rad/s