$A$ uniform thin rod of length $L$ and mass $m$ is lying on a smooth horizontal table. $A$ horizontal impulse $P$ is suddenly applied perpendicular to the rod at one end. The total energy of the rod after the impulse is

Obtain $\tau = I\alpha$ from the angular momentum of a rigid body.

The moment of inertia of a body about a given axis is $1.2 \ kg \cdot m^2$. Initially,the body is at rest. To produce a rotational kinetic energy of $1500 \ J$,an angular acceleration of $25 \ rad/s^2$ must be applied to the body for a duration of ........ $(s)$.

$A$ 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:

$A$ wheel with a moment of inertia of $5 \times 10^{-3} \ kg \cdot m^2$ is rotating at a rate of $20 \ rev/s$. The torque required to bring it to rest in $10 \ s$ is:

$A$ string is wrapped around the rim of a wheel of moment of inertia $0.20\, kg-m^2$ and radius $20\, cm$. The wheel is free to rotate about its axis and initially the wheel is at rest. The string is now pulled by a force of $20\, N$. The angular velocity of the wheel after $5\, s$ will be ....... $rad/s$.