A uniform horizontal beam of weight $120\ \text{N}$ is supported by a pivot at its left end and a vertical cable at its right end. The beam is $2.4\ \text{m}$ long. A load of weight $80\ \text{N}$ is placed $0.60\ \text{m}$ from the pivot.

A point on the rim of a rotating disc is $0.18\ \text{m}$ from the axis. The disc rotates at $420\ \text{rev min}^{-1}$.

The graph shows the variation of angular velocity $\omega$ with time $t$ for a motor shaft. The angular acceleration is uniform over the interval shown.

Three small masses are fixed to a light rigid frame that rotates about an axis perpendicular to the frame. Their distances from the axis are shown.

A flywheel of moment of inertia $0.72\ \text{kg m}^2$ is initially at rest. A constant resultant torque of $4.5\ \text{N m}$ acts on it for $8.0\ \text{s}$.

A student investigates the torque produced on a light gate by applying the same force at the handle at different angles to the radius line from the hinge.

Two equal and opposite tangential forces are applied to a steering wheel to turn it while its centre remains fixed.

Two coaxial turntables are initially separate. Turntable A has moment of inertia $0.30\ \text{kg m}^2$ and angular velocity $+12\ \text{rad s}^{-1}$. Turntable B has moment of inertia $0.20\ \text{kg m}^2$ and angular velocity $-6.0\ \text{rad s}^{-1}$. The turntables are brought into contact and rotate together with common angular velocity $\Omega$. External torque is negligible.

A variable resultant torque acts on a rotor. The graph shows torque $\tau$ against time $t$. Counter-clockwise torque is taken as positive.

A skater rotates with angular speed $3.0\ \text{rad s}^{-1}$ and moment of inertia $4.8\ \text{kg m}^2$. The skater pulls in their arms so that the moment of inertia becomes $3.2\ \text{kg m}^2$. External torque is negligible.

A rigid block floats on a nearly frictionless air table. Two different horizontal forces of the same magnitude may be applied to the block. Force A acts through the centre of mass. Force B acts along a line that does not pass through the centre of mass.

A uniform horizontal beam is hinged to a wall and supported by a cable. A lamp is attached to the beam. The beam is stationary.

The angular speed of a cooling fan is recorded as it speeds up uniformly and then rotates at constant angular speed.

A skater rotates with negligible external torque while pulling their arms closer to the rotation axis. At $t=0$, the skater's angular speed is $1.8\ \text{rad s}^{-1}$. The graph shows how the skater's moment of inertia changes with time.

A torsion wire exerts a restoring torque on a rigid disc when the disc is rotated through a small angular displacement. The graph shows torque as a function of angular displacement. The moment of inertia of the disc is $0.050\ \text{kg m}^2$.

A uniform solid cylinder rolls without slipping from rest down a slope. The vertical drop of its centre of mass is $0.75\ \text{m}$. For a solid cylinder about its central axis, $I=\dfrac{1}{2}MR^2$. Air resistance is negligible.

A variable resultant torque acts on a turntable. The graph shows the torque as a function of time. The turntable has moment of inertia $0.42\ \text{kg m}^2$ and initial angular speed $3.0\ \text{rad s}^{-1}$ in the positive sense.

Four small masses are fixed to a light rotating frame. The frame itself has negligible moment of inertia. A constant resultant torque is then applied about the central axis.

Two coaxial discs rotate freely with opposite senses and are then clamped together. Friction in the clamp is internal to the two-disc system.

A motor exerts a net driving torque on a flywheel as it turns through an angular displacement. The flywheel has moment of inertia $0.25\ \text{kg m}^2$ and initial angular speed $16\ \text{rad s}^{-1}$.

A uniform horizontal beam is hinged to a vertical wall at one end. A cable attached to the other end of the beam makes an angle of $35^\circ$ above the beam. A box is suspended from the beam $2.2\ \text{m}$ from the hinge.

A centrifuge rotor starts from rest. Its angular velocity is increased uniformly, then kept constant, and finally reduced uniformly to rest.

Four identical small masses, each of mass $0.50\ \text{kg}$, are attached to a light rigid rectangular frame. The frame rotates about an axis through its centre and perpendicular to the plane of the frame.

A small satellite in deep space is initially at rest. Two thrusters fire simultaneously, producing a couple about the centre of mass of the satellite. The moment of inertia of the satellite about this axis is $52\ \text{kg m}^2$.

A disc is suspended from a thin torsion wire. When the disc is twisted and released, the wire exerts a restoring torque on the disc given by $\tau=-\kappa\theta$, where $\theta$ is the angular displacement from equilibrium. For this question, $I = 0.084\ \text{kg m}^2$, $\kappa = 0.056\ \text{N m rad}^{-1}$, and the disc is released from rest at $\theta_0 = 0.40\ \text{rad}$.

A small satellite moves in an elliptical orbit around a planet. The planet is much more massive than the satellite. Air resistance is negligible.

Three objects of the same mass and radius roll without slipping down the same ramp. The expression $I=kMR^2$ may be used, where $k=1.0$ for a hoop, $k=0.50$ for a solid cylinder and $k=0.40$ for a solid sphere. The vertical drop of the centre of mass is $0.35\ \text{m}$.

A satellite moves in an elliptical orbit around a planet. The gravitational force acts along the line joining the satellite and the centre of the planet. The table gives data for the satellite at the closest and furthest points of the orbit.

Two coaxial flywheels can rotate freely about the same fixed axle. They are initially separate and are then clamped together. Friction in the clamp acts only between the two flywheels during the joining process.

A turntable of moment of inertia $0.72\ \text{kg m}^2$ rotates initially with angular velocity $4.0\ \text{rad s}^{-1}$ in the positive sense. A variable external torque is applied.

A solid cylinder rolls without slipping from rest down a straight ramp. The moment of inertia of a solid cylinder about its central axis is $I=\frac{1}{2}MR^2$.

A student stands on a rotating platform and holds two identical dumbbells. The platform rotates freely except for a small constant frictional torque. Treat the student and platform, excluding the dumbbells, as having constant moment of inertia.

A light rigid rod is pivoted at its centre and can rotate freely in a horizontal plane. Two identical small masses are fixed to the ends of the rod. A small piece of clay moves horizontally and sticks to one end of the rod in an inelastic collision.

Two masses are connected by a light inextensible string that passes over a pulley. The string does not slip on the pulley. The pulley rotates about a fixed axle with negligible axle friction.