Question

A thin uniform solid wheel is initially rotating with an angular velocity $50\text{rad/s}$. The mass of the wheel is given to be $4\text{kg}$ and the radius of the wheel is $1\text{m}$. If the wheel comes to rest in $10\text{s}$, find the magnitude of the average retarding torque acting on the wheel (in $\text{N-m}$)
(Assume uniform angular retardation)

Answer 1

Given, initial angular velocity of wheel $\left(\omega \right)=50\text{rad/s}$
Mass of the wheel $M=4\text{kg}$
Radius of the wheel $R=1\text{m}$
Moment of inertial of solid disc (wheel) about axis of rotation
$I=\frac{M{R}^2}{2}=2{\text{kg m}}^2$

After $10\text{s}$, wheel comes to rest
Applying $\omega ={\omega }_0+\alpha t$, we get
$0=50-\alpha t$
or $|\alpha |=5{\text{rad/s}}^2$
Thus, magnitude of average retarding torque acting on the wheel is
$|\overrightarrow{\tau }|=I\alpha$
$=2\times 5=10\text{N-m}$