The torque on the square plate of mass $120 \mathrm{g}$ and edge $5.0 \mathrm{cm}$ if it rotates about a diagonal with a uniform angular acceleration of $0.2 \mathrm{rad} {\mathrm{s}}^{-2}$ is $\mathrm{y}\times {10}^{-5} \mathrm{N} \mathrm{m}$. The value of $\mathrm{y}$ is:

A flywheel of moment of inertia $5.0 \mathrm{kg}-\mathrm{m}$ is rotated at a speed of $60 \mathrm{rad} {\mathrm{s}}^{-1}$. Because of the friction at the axle, it comes to rest in $5.0$ minutes. Find

(a) the average torque of the friction.

(b) the total work done by the friction.

(c) the angular momentum of the wheel $1$ minute before it stops rotating.

A light rod of length $1 \mathrm{m}$ is pivoted at its centre and two masses of $5 \mathrm{kg}$ and $2 \mathrm{kg}$ are hanging from the ends as shown. The initial angular acceleration of the rod is $x \mathrm{rad} {\mathrm{s}}^{-2}$ assuming that it was horizontal in the beginning. Find $x$.

A light rod of length $1 \mathrm{m}$ is pivoted at its centre and two masses of $5 \mathrm{kg}$ and $2 \mathrm{kg}$ are hanging from the ends as shown. 

Suppose the rod has a mass of $1 \mathrm{kg}$ distributed uniformly over its length, then find

(a) the initial angular acceleration of the rod.

(b) the tension in the supports to the blocks of mass $2 \mathrm{kg}$ and $5 \mathrm{kg}$.