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 turntable with a moment of inertia of $0.40\ \text{kg m}^2$ is rotating freely at $3.00\ \text{rad s}^{-1}$. A ring of mass $1.2\ \text{kg}$ and radius $0.30\ \text{m}$ is gently dropped concentrically onto the turntable and sticks to it without slipping. Assume no external torques act on the system.

A pizza chef spins a uniform circular dough disc of mass $0.6\ kg$ and radius $0.25\ m$ on his finger. The angular speed is $8.0\ rad\ s^{-1}$. What is the total rotational kinetic energy of the spinning dough?

A student twirls a uniform rod of mass $1.0\ kg$ and length $1.2\ m$ about one end in a vertical plane at a constant angular speed of $2.0\ rad\ s^{-1}$. What is the net force required at the pivot to maintain this motion when the rod is horizontal?

A uniform rod of length $1.2\ \text{m}$ and mass $3.0\ \text{kg}$ is pivoted at one end and allowed to swing freely in a vertical plane, forming a physical pendulum. The moment of inertia of the rod about the pivot is $I = \frac{1}{3}ML^2$.

A ladder leans against a smooth wall, making an angle $\theta$ with the horizontal. If it begins to slip when $\theta = 40°$, what is the coefficient of static friction at the base?