STD 11 - 6. system of particles and rotational motion — NEET STD 11 Science — Question

Initial angular speed, $\omega_0=0 rad / s$

Final angular speed, $\omega=100 rps$

$\Rightarrow \omega=100 \times 2 \pi rad$ $\Rightarrow \omega=200 \pi rad / s$

Time, $t=4 s$

From kinematics:

$\omega =\omega_0+\alpha t$

$\Rightarrow 200 \pi=4 \alpha$

$\Rightarrow \alpha=\frac{200 \pi}{4} rad / s ^2$

where, $\alpha$ is angular acceleration.

Also,

$\theta =\omega_0 t+\frac{1}{2} \alpha t^2$

$\Rightarrow \theta =0+\frac{1}{2} \times \frac{200 \pi}{4} \times 16$

$\Rightarrow \theta =400 \pi$