If $I = 50\,kg-m^2$,then how much torque (in $N-m$) must be applied to stop it in $10\,s$,given its initial angular speed is $20\,rad/s$?

Moment of inertia of a body about an axis is $4 \,kg-m^2$. The body is initially at rest and a torque of $8 \,N-m$ starts acting on it along the same axis. Work done by the torque in $20 \,s$, in joules, is

In the given figure,$r_1$ and $r_2$ are $10 \ cm$ and $20 \ cm$ respectively. If the moment of inertia of the wheel is $1500 \ kg \cdot m^2$,find the angular acceleration.

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 ........ $\hat{k}\, N\cdot m$.

What constant force must be applied tangentially at the equator to stop the Earth's rotation in one day?

$A$ 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 $.5$)