One end of a rod is hinged at $O$. The other end is suspended by a string attached to the ceiling as shown in the figure. If the string is suddenly cut,find the angular acceleration of the rod.

In the figure $(a)$,half of the meter scale is made of wood while the other half is made of steel. The wooden part is pivoted at $O$. $A$ force $F$ is applied at the end of the steel part. In figure $(b)$,the steel part is pivoted at $O'$ and the same force $F$ is applied at the wooden end (in a horizontal plane). Which of the following is true?

$A$ 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 $.5$)

$A$ flywheel gains a speed of $540\ r.p.m.$ in $6\ s$. Its angular acceleration will be

$A$ wheel has a moment of inertia $5 \times 10^{-3} \, kg \, m^2$ and is making $20 \, rev/sec$. The torque needed to stop it in $10 \, sec$ is $............. \times 10^{-2} \, N-m$. (in $\pi$)

$A$ flywheel of mass $25 \,kg$ has a radius of $0.2 \,m$. It is rotating at $240 \,rpm$. What is the torque necessary to bring it to rest in $20 \,s$?