Question

A uniform disc rotating with constant angular acceleration covers $50$ revolutions in the first five seconds after it starts from rest. Calculate the angular acceleration.

• A. $4{\text{rev/s}}^2$
• B. $2{\text{rev/s}}^2$
• C. $8\pi {\text{rev/s}}^2$
• D. $4\pi {\text{rev/s}}^2$

Answer 1

The correct option is A $4{\text{rev/s}}^2$

Given, $\alpha =$ constant (angular acceleration)
$\theta$ is covered in $5$ seconds.
$\theta =50\text{rev}=50\times 2\pi \text{rad}$
$\theta =100\pi \text{rad}$
As we know $\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$
$\Rightarrow 100\pi =0\times t+\frac{1}{2}\alpha \times 5^2$
(${\omega }_0=0$ because it starts from rest)
$\Rightarrow \alpha =8\pi {\text{rad/s}}^2$
or $\alpha =8\pi {\text{rad/s}}^2=\frac{8\pi }{2\pi }{\text{rev/s}}^2=4{\text{rev/s}}^2$