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,

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

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

\(\Rightarrow \theta =400 \pi\)