IB Physics A.4 Rigid Body Mechanics Questionbank

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 plank of mass $8.0\ kg$ and length $4.0\ m$ rests horizontally on two supports placed $0.5\ m$ from each end. A person of mass walks from the center toward one end. At what distance from the center will the plank begin to tip?

A uniform disc of mass $m$ and radius $r$ has a moment of inertia $I=\frac{1}{2}mr^{2}$ about its central axis. The disc is spinning at angular velocity about that axis when it is gently placed on a rough horizontal surface, with its centre initially at rest. Friction acts until the disc rolls without slipping.

A pulley system consists of a solid disc (mass $3.0\ kg$, radius $0.25\ m$) mounted horizontally and free to rotate. A $1.5\ kg$ mass is suspended and allowed to fall, causing the pulley to rotate. What is the angular acceleration of the disc?

A uniform thin rod of mass $1.5\ \text{kg}$ and length $1.2\ \text{m}$ is held in a horizontal position and pivoted at one of its ends. The rod is released from rest and allowed to swing downwards under the influence of gravity. The moment of inertia of a uniform rod about an axis through its end is given by $I = \frac{1}{3}ML^2$.