Physics: Higher Level
Rigid body mechanics — HL Theme A
- 1.
Define torque, and state the two factors that determine the torque produced by a force acting on a rigid body.
[3 marks] · no calculator - 2.
Marking analysis: A learner attempts the following task: “Define torque, and state the two factors that determine the torque produced by a force acting on a rigid body.” Their response addresses only this point: “Defines torque as the turning effect of a force about a pivot or axis of rotation.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator - 3.
A force of 15 N is applied perpendicular to a wrench at a distance of 0.20 m from a bolt. Calculate the torque produced.
[2 marks] - 4.
Marking analysis: A learner attempts the following task: “A force of 15 N is applied perpendicular to a wrench at a distance of 0.20 m from a bolt. Calculate the torque produced.” Their response addresses only this point: “Uses torque τ = Fr (force × perpendicular distance).” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] - 5.
Define moment of inertia, and state one factor (other than mass) that affects the moment of inertia of a rigid body about a given axis.
[2 marks] · no calculator - 6.
Marking analysis: A learner attempts the following task: “Define moment of inertia, and state one factor (other than mass) that affects the moment of inertia of a rigid body about a given axis.” Their response addresses only this point: “Defines moment of inertia as a measure of an object's resistance to angular (rotational) acceleration about a given axis.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] · no calculator - 7.
State the rotational form of Newton's second law, relating torque, moment of inertia and angular acceleration.
[2 marks] · no calculator - 8.
Marking analysis: A learner attempts the following task: “State the rotational form of Newton's second law, relating torque, moment of inertia and angular acceleration.” Their response addresses only this point: “States τ = Iα, where τ is the net torque, I is the moment of inertia, and α is the angular acceleration.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] · no calculator - 9.
A rigid body has moment of inertia 4.0 kg m² about a fixed axis. A net torque of 12 N m is applied. Calculate its angular acceleration.
[2 marks] - 10.
Marking analysis: A learner attempts the following task: “A rigid body has moment of inertia 4.0 kg m² about a fixed axis. A net torque of 12 N m is applied. Calculate its angular acceleration.” Their response addresses only this point: “Uses τ = Iα.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] - 11.
Define angular momentum, and state the principle of conservation of angular momentum.
[2 marks] · no calculator - 12.
Marking analysis: A learner attempts the following task: “Define angular momentum, and state the principle of conservation of angular momentum.” Their response addresses only this point: “Defines angular momentum as L = Iω, the product of moment of inertia and angular velocity.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] · no calculator - 13.
An ice skater spinning with arms outstretched has moment of inertia 4.0 kg m² and angular velocity 2.0 rad s⁻¹. She pulls her arms in, reducing her moment of inertia to 1.0 kg m². Calculate her new angular velocity, using conservation of angular momentum.
[3 marks] - 14.
Marking analysis: A learner attempts the following task: “An ice skater spinning with arms outstretched has moment of inertia 4.0 kg m² and angular velocity 2.0 rad s⁻¹. She pulls her arms in, reducing her moment of inertia to 1.0 kg m². Calculate her new angular velocity, using conservation of angular momentum.” Their response addresses only this point: “Uses conservation of angular momentum: I₁ω₁ = I₂ω₂.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] - 15.
State the condition(s) required for a rigid body to be in rotational equilibrium.
[2 marks] · no calculator - 16.
Marking analysis: A learner attempts the following task: “State the condition(s) required for a rigid body to be in rotational equilibrium.” Their response addresses only this point: “States that the net (resultant) torque acting on the body about any point must be zero.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] · no calculator - 17.
State the equation for rotational kinetic energy in terms of moment of inertia and angular velocity, and calculate the rotational kinetic energy of a wheel with moment of inertia 2.0 kg m² spinning at 5.0 rad s⁻¹.
[3 marks] - 18.
Marking analysis: A learner attempts the following task: “State the equation for rotational kinetic energy in terms of moment of inertia and angular velocity, and calculate the rotational kinetic energy of a wheel with moment of inertia 2.0 kg m² spinning at 5.0 rad s⁻¹.” Their response addresses only this point: “States rotational kinetic energy = ½Iω².” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] - 19.
A uniform beam of weight 200 N and length 4.0 m is supported horizontally by a pivot at one end and a vertical cable at the other end. Calculate the tension in the cable, taking torques about the pivot.
[4 marks] - 20.
Marking analysis: A learner attempts the following task: “A uniform beam of weight 200 N and length 4.0 m is supported horizontally by a pivot at one end and a vertical cable at the other end. Calculate the tension in the cable, taking torques about the pivot.” Their response addresses only this point: “States that the weight acts at the centre of the uniform beam, 2.0 m from the pivot.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] - 21.
Two point masses, 2.0 kg and 3.0 kg, are attached to the ends of a light rigid rod, at distances of 0.40 m and 0.60 m respectively from a pivot at the rod's centre of rotation. Calculate the total moment of inertia of this system about the pivot.
[4 marks] - 22.
Marking analysis: A learner attempts the following task: “Two point masses, 2.0 kg and 3.0 kg, are attached to the ends of a light rigid rod, at distances of 0.40 m and 0.60 m respectively from a pivot at the rod's centre of rotation. Calculate the total moment of inertia of this system about the pivot.” Their response addresses only this point: “States that for a system of point masses, I = Σmr².” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] - 23.
A net torque of 8.0 N m acts on a rigid body for 5.0 s. Calculate the change in angular momentum produced, and state the equation used.
[3 marks] - 24.
Marking analysis: A learner attempts the following task: “A net torque of 8.0 N m acts on a rigid body for 5.0 s. Calculate the change in angular momentum produced, and state the equation used.” Their response addresses only this point: “States that angular impulse = torque × time = ΔL.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] - 25.
A solid sphere of mass 2.0 kg and radius 0.10 m rolls without slipping along a horizontal surface at a linear speed of 3.0 m/s. Given that its moment of inertia about its central axis is I = (2/5)mr², and that for rolling without slipping v = ωr, calculate its total kinetic energy (translational plus rotational).
[5 marks] - 26.
Marking analysis: A learner attempts the following task: “A solid sphere of mass 2.0 kg and radius 0.10 m rolls without slipping along a horizontal surface at a linear speed of 3.0 m/s. Given that its moment of inertia about its central axis is I = (2/5)mr², and that for rolling without slipping v = ωr, calculate its total kinetic energy (translational plus rotational).” Their response addresses only this point: “Calculates the translational kinetic energy: ½mv² = ½ × 2.0 × 3.0² = 9.0 J.” Evaluate the response against the complete 5-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[5 marks] - 27.
A wheel completes one full rotation every 0.50 s. Calculate its angular velocity.
[2 marks] - 28.
Marking analysis: A learner attempts the following task: “A wheel completes one full rotation every 0.50 s. Calculate its angular velocity.” Their response addresses only this point: “Uses ω = 2π/T.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[2 marks] - 29.
A solid disk and a thin hoop (ring) have the same mass and the same radius, and both rotate about their central axis. State which has the greater moment of inertia, and explain why, in terms of the distribution of mass.
[3 marks] · no calculator - 30.
Marking analysis: A learner attempts the following task: “A solid disk and a thin hoop (ring) have the same mass and the same radius, and both rotate about their central axis. State which has the greater moment of inertia, and explain why, in terms of the distribution of mass.” Their response addresses only this point: “States that the hoop has the greater moment of inertia.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator