$A$ wheel of radius $0.4 \ m$ can rotate freely about its axis as shown in the figure. $A$ string is wrapped around its circumference,and a weight of $4 \ kg$ is suspended from it. Due to the torque,an angular acceleration of $8 \ rad \ s^{-2}$ is produced. The moment of inertia of the wheel is = $...... \ kg \ m^2$ $(g = 10 \ ms^{-2})$

$A$ wheel is at rest in a horizontal position. Its moment of inertia about the vertical axis passing through its centre is $I$. $A$ constant torque $\tau$ acts on it for $t$ seconds. The change in rotational kinetic energy is:

If a constant torque acts on an object,then the object:

If there is a change of angular momentum from $1 \, J \cdot s$ to $4 \, J \cdot s$ in $4 \, s$, then the torque is

$A$ 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 $3 \ s$?

Consider a $20\, kg$ uniform circular disk of radius $0.2\, m$. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force $F = 20\, N$ through a massless string wrapped around its periphery as shown in the figure. Suppose the disk makes $n$ number of revolutions to attain an angular speed of $50\, rad/s$. The value of $n$,to the nearest integer,is.......... [Given: In one complete revolution,the disk rotates by $6.28\, rad$]