A.4 Rigid body mechanics (HL only) Questionbank

A rotating platform in a physics lab has a moment of inertia $I = 0.50\ \text{kg m}^2$ and is initially rotating at $6.0\ \text{rad s}^{-1}$. A student drops a lump of clay of mass $0.20\ \text{kg}$ onto the platform at a distance of $0.30\ \text{m}$ from the axis. The clay sticks to the platform.

A yo-yo of mass $m$ and radius $r$ is released from rest and allowed to fall vertically while unwinding. If its moment of inertia is $I = \frac{1}{2}mr^2$, what is the linear acceleration of its center of mass?

A rod of length $L$ and mass $M$ is pivoted at one end and released from rest in a horizontal position. What is its angular velocity just before it strikes the vertical?

A disc of moment of inertia $I$ spinning at angular velocity $\omega$ is placed on a horizontal surface with friction and allowed to roll without slipping. After some time, it transitions into pure rolling motion. What happens to its final angular velocity?

A flywheel rotates with an initial angular velocity of $12.0\ \text{rad s}^{-1}$ and comes to rest after 8.0 seconds due to a constant frictional torque. The moment of inertia of the flywheel is $0.80\ \text{kg m}^2$.

A student investigates the torque $(\tau)$ produced by applying varying forces $(F)$ at different distances $(r)$ from the pivot of a rigid beam. The following data were recorded:

The relationship between torque, force, and distance is given by:

where:

• $\tau$ is the torque,
• $r$ is the perpendicular distance from the pivot,
• $\quad F$ is the applied force.

A billiard ball of radius $R$ and mass $M$ is struck by a horizontal cue stick at a height $h$ above the billiard table. The moment of inertia for a sphere is given by $I=\frac{2}{5}MR^2$. The cue stick strikes the ball with a force $F$ during an interval $\Delta t$.

A uniform beam of mass $20\ kg$ and length $6.0\ m$ is supported horizontally by two ropes. One rope is $1.0\ m$ from the left end, and the other is $1.0\ m$ from the right end. A $40\ kg$ person stands $1.0\ m$ from the left end. What is the tension in the right rope?

An object of mass $m$ makes $n$ revolutions per second around a circle of radius $r$ at a constant speed. What is the kinetic energy of the object?

A solid uniform rod of length $L=2.0 \ m$ and mass $M=3.0 \ kg$ is pivoted at one end. The rod can rotate freely in a vertical plane about this pivot. A force of $F=10 \ N$ is applied perpendicular to the rod at its free end.