Question

A wheel has initial angular speed of $\pi \text{rad/s}$. A constant force is acting on wheel to stop it. If wheel covers $\theta =\frac{\pi }{2}\text{rad}$ before coming to rest, find the magnitude of angular acceleration of the wheel.

• A. $\frac{\pi }{2}{\text{rad/s}}^2$
• B. $\frac{\pi }{3}{\text{rad/s}}^2$
• C. $\pi {\text{rad/s}}^2$
• D. $\frac{\pi }{4}{\text{rad/s}}^2$

Answer 1

The correct option is C $\pi {\text{rad/s}}^2$

Given:
Initial angular speed of wheel ${\omega }_o=\pi \text{rad/s}$
As wheel stops
$\therefore$ Final angular speed of wheel $\omega =0\text{rad/s}$
Angle covered before coming to rest $\theta =\frac{\pi }{2}\text{rad}$
Let constant angular acceleration of wheel is $\left(\alpha \right)\text{rad/s}$
Using
${\omega }^2={\omega }_o^2+2\alpha \theta$
$0={\pi }^2+2\times \alpha \times \frac{\pi }{2}$
$\Rightarrow \alpha =-\pi {\text{rad/s}}^2$
Here $-ve$ sign indicates that wheel has angular acceleration opposite to it's angular velocity.
$|\alpha |=\pi {\text{rad/s}}^2$