Dynamics of Rotational Motion about a Fixed Axis

A particle performs uniform circular motion with an angular momentum $L$. If the frequency of particle motion is doubled and its kinetic energy is halved, the angular momentum becomes,

Two bodies have their moments of inertia $I$ and $2I$, respectively, about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio,

A rod of mass $M$ and length $L$ is placed in a horizontal plane with one end hinged about the vertical axis. A horizontal force $F=\frac{Mg}{2}$ is applied at a distance $\frac{5L}{6}$ from the hinged end. The angular acceleration of the rod will be

A Merry-go-round, made of a ring-like platform of radius $\mathbf{R}$ and mass $\mathrm{M}$, is revolving with angular speed $\omega$. A person of mass $M$ is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round afterwards is

Which of the following increases the moment of force on an object?

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass $5 \mathrm{g}$ are put one on top of the other at the $12$ $\mathrm{cm}$ mark, the stick is found to be balanced at $45$ $\mathrm{cm}$. The mass of the meter stick is:

A rigid rod of length $2\mathrm{L}$ is acted upon by some forces. All forces labelled $\mathrm{F}$ have the same magnitude. Which cases have a non-zero net torque acting on the rod about its center?

The force $7\widehat{\mathrm{i}}+3\widehat{\mathrm{j}}-5\widehat{\mathrm{k}}$ acts on a particle whose position vector is $\widehat{\mathrm{i}}-\widehat{\mathrm{j}}+\widehat{\mathrm{k}}$. What is the torque of a given force about the origin?