Physics - Rotation Question with Solution | TestHub

The angular acceleration is given by $\alpha =\frac{d\omega }{dt}=t-1$.

Integrating, $\omega =\int (t-1)dt=\frac{t^2}{2}-t+C$.

Since the body is initially at rest, $\omega (0)=0$, so $C=0$.

Thus, $\omega (t)=\frac{t^2}{2}-t$.

At $t=2$ s, $\omega (2)=\frac{2^2}{2}-2=2-2=0$. So, the disc is at rest at $t=2$ s.

For $0<t<1$ s, $\alpha <0$ (clockwise acceleration).

For $1<t<2$ s, $\alpha >0$ (anticlockwise acceleration), but $\omega <0$ (clockwise rotation), so it decelerates.

For $t>2$ s, $\alpha >0$ and $\omega >0$, so it accelerates anticlockwise.

All options are correct.