If $I$,$\alpha$,and $\tau$ are the moment of inertia,angular acceleration,and torque of an object,respectively,and the object is rotating about an axis with an angular velocity $\omega$,then:

$A$ uniform rod of length $l$,hinged at the lower end,is free to rotate in the vertical plane. If the rod is held vertically in the beginning and then released,what is the angular acceleration of the rod when it makes an angle of $45^{\circ}$ with the horizontal? (Given: Moment of inertia $I = ml^2/3$)

The moment of inertia of a wheel rotating about an axis is $3 \times 10^2 \ kg \ m^2$ and it has a constant angular speed of $4.6 \ rad \ s^{-1}$. If a retarding torque of $6.9 \times 10^2 \ N \ m$ is applied to the wheel,in how many seconds will the wheel come to rest?

$A$ same torque is applied to a disc and a ring of equal mass and radii. Then:

$A$ thin uniform stick of length $l$ and mass $m$ is held horizontally with its end $B$ hinged on the edge of a table. Point $A$ is suddenly released. The acceleration of the centre of mass of the stick at the time of release is:

An electric motor is started from rest to produce a torque. It acquires an angular acceleration given by $\alpha = 3t - t^2$. The angular acceleration becomes zero after $2 \ s$. Calculate the angular velocity after $6 \ s$.