A force of 18 N is applied to a spanner at a distance of 0.25 m from the nut. The angle between the spanner and the force is 60°.

A uniform beam is in rotational equilibrium about a pivot.

A constant resultant torque acts on a rigid body whose moment of inertia remains constant.

A wheel rotates at 240 revolutions per minute.

Two point masses of 0.20 kg are fixed to a light rod, each 0.30 m from an axis through the rod’s centre and perpendicular to the rod.

A resultant torque of 6.0 N m acts on a flywheel of moment of inertia 1.5 kg m².

A disc of moment of inertia 0.40 kg m² rotates clockwise at 12 rad s⁻¹.

A flywheel has moment of inertia 2.0 kg m² and angular speed 5.0 rad s⁻¹.

A horizontal force of 35 N is applied to the end of a door at a distance of 0.82 m from its hinges. The force makes an angle of 70° to the surface of the door.

A pair of equal and opposite forces act on a rigid plate along parallel lines of action that do not coincide.

A turntable starts from rest and has a uniform angular acceleration of 3.0 rad s⁻² for 4.0 s.

Two wheels have the same mass and radius. Wheel X has most of its mass near the axle; wheel Y has most of its mass near the rim.

A skater rotates with arms extended. The skater then pulls the arms in so that the moment of inertia decreases by a factor of 2. No external torque acts.

A constant torque of 0.80 N m acts on a rotor for 5.0 s.

Two equal and opposite horizontal forces of magnitude 12 N act on a rigid body. Their parallel lines of action are separated by 0.40 m.

A uniform metre rule of weight 1.2 N is pivoted at the 40 cm mark. A 2.0 N weight is hung at the 10 cm mark.

A centrifuge rotor increases its angular speed uniformly from 120 rad s⁻¹ to 300 rad s⁻¹ in 6.0 s.

Four small masses are fixed at the corners of a light square frame of side 0.40 m. Each mass is 0.15 kg. The axis of rotation passes through the centre of the square and is perpendicular to its plane.

A pulley has moment of inertia 0.12 kg m². A constant frictional torque of 0.18 N m opposes its rotation while a driving torque of 0.66 N m acts in the opposite sense.

A rotor has moment of inertia 0.75 kg m² and rotates anticlockwise at 20 rad s⁻¹. Clockwise is taken as positive.

A disc rotates with constant angular speed 8.0 rad s⁻¹. A point P is 0.25 m from the axis.

A student records the angular speed of a turntable as it starts from rest.

A torque sensor records the resultant torque on a wheel during a short collision with a brake pad.

A solid cylinder with (I=\frac{1}{2}MR^2) rolls without slipping with centre-of-mass speed (v).

Two coaxial discs are brought into contact and rotate together after slipping. Disc 1 has (I) and angular speed (+3\omega). Disc 2 has (2I) and angular speed (-\omega).

A point on the rim of a wheel has tangential speed 6.0 m s⁻¹ and centripetal acceleration 18 m s⁻².

A wheel rotating at 15 rad s⁻¹ is brought uniformly to rest in 5.0 revolutions.

A rotating platform of moment of inertia 5.0 kg m² rotates freely at 1.8 rad s⁻¹. A child standing on it moves inward, reducing the total moment of inertia of the child-platform system from 8.0 kg m² to 6.0 kg m². External torque is negligible.

A variable braking torque acts on a wheel for 3.0 s. The average torque is 2.5 N m opposite to the positive direction. The wheel has moment of inertia 0.50 kg m² and initial angular speed +18 rad s⁻¹.

A hoop of mass (M) and radius (R) rolls without slipping at speed (v). The moment of inertia of a hoop is (I=MR^2).

A horizontal force is applied to a block whose centre of mass is above the line of action of the force. The block rests on a rough horizontal surface and may start to tip.

A wheel is accelerated from rest by a constant torque of 3.0 N m through an angular displacement of 20 rad. Resistive torques are negligible.

A rigid rotor is acted on by different known torques. Its angular acceleration is measured for each torque.

A class investigates rolling without slipping by releasing objects from the same height on a ramp. The table gives repeated descent times for a hoop, a solid cylinder and a solid sphere of the same mass and radius.

A student attaches identical small masses at different distances from the centre of a light rotating frame. The table shows the measured angular acceleration for the same applied torque.

A rolling ball is filmed as it moves along a horizontal track without slipping. The graph shows the position of its centre of mass against time.

A solid sphere of mass 0.60 kg and radius 0.050 m rolls without slipping. Its centre of mass has speed 2.0 m s⁻¹. For a solid sphere, (I=\frac{2}{5}MR^2).

Two satellites orbit the same planet in elliptical orbits. At one point a satellite is closer to the planet than at another point. Assume the torque about the planet’s centre is negligible.

Two coaxial flywheels are coupled by a clutch. The table gives their moments of inertia and angular speeds immediately before coupling. After coupling, they rotate together.

A non-uniform horizontal beam is supported by two vertical supports. The table gives measured upward support forces for different positions of a hanging load.

A turntable is programmed to rotate through a fixed angle. The graph shows angular acceleration against time.

A solid cylinder rolls without slipping from rest down a ramp of vertical height (h). Its moment of inertia about its central axis is (I=\frac{1}{2}MR^2).

A uniform solid disc and a thin hoop have the same mass (M) and radius (R). They are each mounted on frictionless axles through their centres. The moment of inertia of the disc is (\frac{1}{2}MR^2), and that of the hoop is (MR^2). The same constant torque ( au) is applied to each from rest for the same time (t).

A flywheel is spun up by a motor. The graph shows the rotational kinetic energy stored in the flywheel against the square of its angular speed.

Two coaxial flywheels are initially separated. Flywheel A has moment of inertia (0.30, ext{kg m}^2) and angular speed (+24, ext{rad s}^{-1}). Flywheel B has moment of inertia (0.20, ext{kg m}^2) and angular speed (-12, ext{rad s}^{-1}). They are then coupled and rotate together.

A light string is wound around a uniform solid cylinder of radius (R), mass (M), and moment of inertia (I=\frac{1}{2}MR^2). The cylinder is mounted on a frictionless axle. The string is pulled with a constant force (F), causing the cylinder to rotate from rest without the string slipping.

A uniform horizontal beam of length 4.0 m and weight 120 N is hinged to a wall at one end. A cable attached to the other end makes an angle of 35° above the beam. A 200 N sign hangs from the beam 3.0 m from the hinge.

A wheel starts from rest and accelerates uniformly for 6.0 s until it reaches 18 rad s⁻¹. It then rotates at this constant angular speed. A point on the rim is 0.40 m from the axis.

A rotor has initial moment of inertia (I_i=0.80, ext{kg m}^2) and initial angular speed (+10, ext{rad s}^{-1}). While a motor applies a constant external torque of (+3.0, ext{N m}) for 4.0 s, movable masses in the rotor shift outward so that the final moment of inertia is (1.20, ext{kg m}^2).

A ball is rolled up a ramp without slipping. It has mass (M), radius (R), initial centre-of-mass speed (v_0), and moment of inertia (I=kMR^2), where (k) is a constant for the shape.