$A$ constant torque acting on a wheel changes its angular momentum from $A_0$ to $4A_0$ in $4 \ s$. The magnitude of the torque is:

At time $t = 0$,a $2\, kg$ particle has position vector $\vec{r} = (4\hat{i} - 2\hat{j})\, m$ relative to the origin. Its velocity is given by $\vec{v} = 2t^2\hat{i}\, m/s$. The torque acting on the particle about the origin at $t = 2\, s$ is ........ $\hat{k}\, N\cdot m$.

$A$ circular disc of diameter $0.8 \ m$ and mass $4 \ kg$ is rolling on a smooth horizontal plane. If $2.56 \ N \ m$ torque is acting on the disc,then its angular acceleration is

The angular momentum of a wheel changes from $2L$ to $5L$ in $3$ seconds. The magnitude of the torque acting on the wheel is:

$A$ pulley has the shape of a uniform solid disc of mass $2 \ kg$ and radius $0.5 \ m$. $A$ string is wrapped over its rim and is pulled by a force of $2.5 \ N$. The pulley is free to rotate about its axis. Initially,the pulley is at rest. Find the angular velocity of the pulley just after $10 \ s$. (in $rad/s$)

$A$ constant torque of $31.4 \, N \cdot m$ is applied to a pivoted wheel. If the angular acceleration of the wheel is $4\pi \, rad/s^2$,then the moment of inertia of the wheel is ....... $kg \cdot m^2$. (in $.5$)