Angular Momentum — Prelims Questions

A particle of mass $m$ is projected with a velocity $v$ at an angle $\theta$ with the horizontal from the ground. The angular momentum of the particle about the point of projection when it is at its maximum height $H$ is:

A uniform circular disc of mass $M$ and radius $R$ is rotating about its axis with angular speed $\omega$. If two particles, each of mass $m$, are gently placed at diametrically opposite points on its rim, the new angular speed of the disc will be:

A constant torque of $20\,\text{N\cdot m}$ is applied to a wheel. If its angular momentum changes from $10\,\text{J\cdot s}$ to $70\,\text{J\cdot s}$ in a certain time, what is that time interval?

A uniform rod of mass $M$ and length $L$ is pivoted at one end and released from rest in a horizontal position. The angular momentum of the rod about the pivot when it is in the vertical position is:

A particle of mass $m$ is moving in a circular path of radius $r$ with a constant speed $v$. The angular momentum of the particle about the center of the circle is:

A solid cylinder of mass $M$ and radius $R$ is rotating about its own axis with angular speed $\omega$. Its angular momentum is $L$. If its radius is doubled and mass is halved, what will be its new angular momentum if it rotates with the same angular speed?