If a disc of mass $M$ and radius $R$ rotates with an angular acceleration $a$, the torque acting on the disc is

The variation of angular acceleration $\alpha$ of a point on a rigid body rotating about a fixed axis with time $t$ is shown in the figure. What is the sense of rotation of the rod? (Assume clockwise as negative)

$A$ wheel rotates at $720 \ rpm$ about an axis passing through its center. It is brought to rest by applying a constant torque for $8 \ s$. What is the value of the torque in $Nm$? (Given: $I = \frac{24}{\pi} \ kg \cdot m^2$)

$A$ wheel is subjected to a torque of $1000 \ N-m$ and rotates with a moment of inertia of $200 \ kg-m^2$ about an axis passing through its center. What will be the angular velocity of the wheel after $3 \ s$?

$A$ body rotating at $20 \ rad/s$ is acted upon by a constant torque providing it a deceleration of $2 \ rad/s^2$. At what time will the body have kinetic energy same as the initial value if the torque continues to act?

Find the ratio of linear acceleration $(a)$ to angular acceleration $(\alpha)$ of the center of mass $(COM)$ for the given diagram. Given: $m = 2 \, kg$,$r = 10 \, cm = 0.1 \, m$,and force $F = 20 \, N$ applied at the center.