$A$ uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A.$ The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $ml^2/3$,the initial angular acceleration of the rod will be:

$A$ torque of $10^5 \ N \cdot m$ is applied to a disc of mass $10 \ kg$ and radius of gyration $50 \ m$. What is the value of the angular acceleration in $rad/s^2$?

Consider a particle of mass $m$ having linear momentum $\vec{p}$ at position $\vec{r}$ relative to the origin $O$. Let $\vec{L}$ be the angular momentum of the particle with respect to the origin. Which of the following equations correctly relate $\vec{r}, \vec{p}$ and $\vec{L}$?

$A$ pulley of radius $10 \ cm$ has a moment of inertia of $10^{-3} \ kg \ m^2$ about its geometric axis. $A$ time-varying tangential force $F = (0.5t - 0.3t^2) \ N$ is applied to its rim. The pulley is initially at rest. If $t$ is in seconds,what will be the angular acceleration of the pulley at $t = 3 \ s$ in $rad \ s^{-2}$?

$A$ circular disc of radius $2 \ m$ is rotating at $240 \ rpm$. If a torque is applied to the disc, it slows down at a rate of $\pi \ rad/s^2$. How long will it take to stop? How many revolutions will the disc complete before coming to rest?

$A$ force of $1 \ N$ is applied at the free edge of a door of width $1.6 \ m$ to open it. If the door is to be opened by applying force at a point $0.4 \ m$ away from the hinges (axis of rotation),then the force required is ...... $N$.