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Option C: The Physics of Sports

Torque, angular momentum and its conservation

  • 3 things to know
  • A2 Unit 4 Section B

Overview

Recall questions on Torque, angular momentum and its conservation.

What you need to know

Answer each one before you reveal it.

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Key term

Why do two athletes of the same mass need different torques to reach the same rate of spin in the same time?

Key term

State the unit of angular momentum in SI base units.

Key term

How does a diver acquire angular momentum in the first place, given that it cannot change in the air?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is the unit of torque, and which linear quantity does torque correspond to?

    Model answer

    Torque is measured in N m, and it corresponds to force in linear motion. It is the quantity that produces angular acceleration.

  2. 2

    A wheel of moment of inertia 0.25 kg m² is given an angular acceleration of 12 rad s⁻². Calculate the torque applied.

    Model answer

    τ = Iα = 0.25 × 12 = 3.0 N m. Substituting back, 3.0 ÷ 0.25 returns an angular acceleration of 12 rad s⁻².

  3. 3

    A gymnast swinging on a high bar has a moment of inertia of 12 kg m² about the bar. A torque of 84 N m acts. Calculate the angular acceleration.

    Model answer

    α = τ/I = 84 ÷ 12 = 7.0 rad s⁻². Substituting back, 12 × 7.0 returns a torque of 84 N m.

  4. 4

    Why do two athletes of the same mass need different torques to reach the same rate of spin in the same time?

    Model answer

    The torque required is the moment of inertia times the angular acceleration, and with equal masses the moment of inertia depends on how the mass is distributed about the axis. The athlete with the longer limbs or the more extended shape needs the larger torque.

  5. 5

    State the unit of angular momentum in SI base units.

    Model answer

    Angular momentum is measured in kg m² s⁻¹.

  6. 6

    A diver leaves the board in a straight position with a moment of inertia of 3.5 kg m² and an angular velocity of 2.0 rad s⁻¹. Calculate the angular momentum.

    Model answer

    L = Iω = 3.5 × 2.0 = 7.0 kg m² s⁻¹. Substituting back, 7.0 ÷ 3.5 returns an angular velocity of 2.0 rad s⁻¹.

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