Answer 1

Given

t = 4s

Initial angular velocity = \[\omega_0 = 0\]

Final angular velocity = \[\omega = 100 \text{ rev/s}\]

\[\omega = \omega_0 + \alpha t\]

\[\alpha = \frac{\omega}{t}\]

\[\alpha = \frac{100}{4}\text{ rev/ s}^2 = 25\text{ rev/ s}^2 \]

Now, we have

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

\[ \Rightarrow \theta = \frac{1}{2} \times 25 \times 16\]

\[ = 200^\circ\]

\[ \Rightarrow \theta = 200 \times 2\pi\text{ radians}\]

\[ = 400\pi\text{ radians}\]