Question

A wheel of radius $10cm$ can rotate freely about an axis passing through its centre. A force $20N$ acts tangentially at the rim of wheel. If moment of inertia of wheel is $0.5kg{m}^2$, its angular acceleration is:

• A. $2rad/s^2$
• B. $2.5rad/s^2$
• C. $4rad/s^2$
• D. $5rad/s^2$

Answer 1

The correct option is C $4rad/s^2$

Torque on the wheel $\tau =\overrightarrow{F}\times \overrightarrow{R}$
as F is applied at rim.
$\Rightarrow \tau =20\times 0.1=2Nm$
Moment of Inertia $I=0.5kg{m}^2$
$\tau =I\alpha$
$\Rightarrow \alpha =\frac{\tau }{I}=\frac{2}{0.5}=4rad/s^2$