Conservation of Angular Momentum — Prelims Questions

A uniform circular disc of mass $M$ and radius $R$ is rotating with an angular velocity $\omega_0$ about its axis. Two point masses, each of mass $m$, are gently placed at the opposite ends of a diameter of the disc. What is the new angular velocity of the system?

A child stands on a freely rotating platform with his arms extended. He holds a $2,\text{kg}$ mass in each hand. The angular speed of the platform is $10,\text{rad/s}$. The moment of inertia of the child and platform without the masses is $2,\text{kg m}^2$. When the child pulls his arms in, the masses are $0.2,\text{m}$ from the axis of rotation. Initially, the masses are $1,\text{m}$ from the axis. What is the new angular speed of the platform?

Which of the following scenarios best illustrates the conservation of angular momentum?

A uniform rod of mass $M$ and length $L$ is pivoted at one end and is free to rotate in a horizontal plane. Initially, it is at rest. A point mass $m$ moving with velocity $v$ perpendicular to the rod strikes the free end of the rod and sticks to it. What is the angular velocity of the rod-mass system immediately after the collision?

A planet of mass $m$ is revolving around the Sun in an elliptical orbit. If $v_p$ and $v_a$ are the velocities of the planet at the perihelion (closest point) and aphelion (farthest point) respectively, and $r_p$ and $r_a$ are the corresponding distances from the Sun, then which of the following relations is correct?

A merry-go-round of radius $R = 2,\text{m}$ and moment of inertia $I_{mg} = 100,\text{kg m}^2$ is rotating at an angular speed of $\omega_0 = 2,\text{rad/s}$. A child of mass $m = 25,\text{kg}$ jumps onto the merry-go-round at its edge. What is the new angular speed of the merry-go-round?

A solid cylinder of mass $M$ and radius $R$ is rotating about its axis with angular speed $\omega$. Another identical solid cylinder is gently dropped on the first cylinder, such that their axes coincide. What is the common angular speed of the combined system?