Topic 1.4: Rigid body mechanics (HL) Questions

A flywheel used to store energy has a moment of inertia of 12 kg m² and spins at 40 rad s⁻¹. (a) Determine the rotational kinetic energy stored. (b) State what happens to this energy as the flywheel slows down to drive a machine.

A uniform metre rule is pivoted at its 30 cm mark. A 2.0 N weight hangs at the 10 cm mark. At which distance from the pivot must a 1.0 N weight hang on the other side to balance the rule? (Ignore the rule's own weight.)

A wheel rolls along the ground without slipping at a constant linear speed. Which quantity increases linearly with time?

Two discs spin with the same angular momentum L. Disc X has moment of inertia I, and disc Y has moment of inertia 4I. What is the ratio of the rotational kinetic energy of X to that of Y?

A point mass of 0.50 kg is fixed at the end of a light rod 0.40 m long and rotates about an axis through the other end. What is its moment of inertia about that axis?

A uniform horizontal beam of length 4.0 m and weight 300 N is hinged to a wall at one end and held up by a vertical cable at the other end. (a) Determine the tension in the cable. (b) State why taking torques about the hinge is the convenient choice.

A wheel starts from rest and reaches an angular velocity of 10 rad s⁻¹. Its moment of inertia is 0.50 kg m². What is the change in its angular momentum?

A net torque of 12 N m acts on a wheel of moment of inertia 3.0 kg m². What is the angular acceleration of the wheel?

Two identical horizontal forces of 5.0 N act in opposite directions on the two ends of a 0.40 m rod, forming a couple. Each force is perpendicular to the rod. What is the SI unit and magnitude of the resulting torque (couple)?

Four objects have the same mass M and same radius R and rotate about their central axes. Which has the GREATEST moment of inertia?

A disc accelerates uniformly from rest to an angular velocity of 12 rad s⁻¹ in 3.0 s. What is the angle, in radians, through which it turns in this time?

A grinding wheel (moment of inertia 0.040 kg m²) starts from rest. A constant net torque of 0.20 N m acts on it. Determine the angular velocity of the wheel after 3.0 s.

A potter's wheel starts from rest and is brought up to a steady angular velocity of 30 rad s⁻¹ in 5.0 s, accelerating uniformly.
(a) Determine the angular acceleration of the wheel.
(b) Determine the number of complete revolutions the wheel makes during this time.

A wheel of radius 0.32 m rolls along the ground without slipping and completes exactly 8.0 revolutions.
Determine the distance the wheel travels along the ground.

A mechanic applies a 60 N force to the end of a 0.25 m spanner. The force is directed at an angle of 65° to the spanner arm.
(a) Determine the torque produced about the bolt.
(b) State the angle at which the same force would produce the maximum torque, and calculate that maximum.

A turntable starts from rest and is given a constant angular acceleration of 3.0 rad s⁻². Its moment of inertia is 0.40 kg m².

Determine the angular momentum of the turntable after it has been accelerating for 5.0 s.

A solid uniform sphere and a thin ring have the same mass M = 1.5 kg and the same radius R = 0.12 m. For a solid sphere I = 2/5 MR²; for a thin ring I = MR². Both rotate about an axis through their centre.
(a) Calculate the moment of inertia of each object.
(b) State which is harder to set spinning, and why.

A solid disc of moment of inertia 0.25 kg m² spins at 20 rad s⁻¹. A torque is applied that, acting over a time, changes its angular velocity to 32 rad s⁻¹.

Calculate the angular impulse (change in angular momentum) delivered to the disc, and state its SI unit.

Two equal and opposite forces of 8.0 N act on opposite edges of a steering wheel of diameter 0.36 m, forming a couple that turns the wheel. The forces act tangentially (perpendicular to the radius at each edge).
Determine the total turning torque (the couple) on the wheel.

A force of 20 N acts at a point 0.50 m from a pivot, at an angle of 30° to the line joining the point to the pivot. What is the torque about the pivot?