Moment of Inertia by Integration and the Parallel-Axis Theorem · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Why shape sets spin resistance

Science · Forces & Motion · ages 20-21
Name ______________________   Date ____________

  1. The same body can have different moments of inertia about different axes.

    Circle one:   True   False

  2. Moment of inertia weights each bit of mass by which power of its distance from the axis?

    • Distance to the first power
    • Distance squared
    • Distance cubed

  3. A thin hoop and a solid disc have the same mass and radius. A thin rod has the same mass and length equal to the diameter. Which has the largest moment of inertia about its central perpendicular axis?

    • Solid disc
    • Thin rod through its centre
    • Thin hoop, mass at rim

  4. A rod has centre of mass moment of inertia 1 kilogram metre squared and mass 3 kilograms. What does the parallel-axis theorem give about a parallel axis at perpendicular offset 1 metre?

    • 1 plus 3 times 1 squared, which is 4
    • 1 times 3 times 1, which is 3
    • 1 minus 3, which is negative 2

  5. A flywheel has I equal to 2 kilogram metres squared and spins with omega 3 radians per second. What is its rotational kinetic energy, in joules?

    Answer: ______________

  6. Shifting the axis away from the centre of mass always lowers the moment of inertia.

    Circle one:   True   False

  7. A hoop of mass 2 kilograms and radius 3 metres has I equal to M R squared. What is I, in kilogram metres squared?

    Answer: ______________

  8. A student computes I by adding mass times distance, not squared. For a thin hoop they get MR. What do they get for a uniform disc of the same mass and radius about the central perpendicular axis?

    • MR, the same as the hoop
    • 2MR over 3, less than the hoop
    • MR over 2, half the hoop
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Why shape sets spin resistance W1-mt_VFRk1WIzAK-s1

  1. True · Mass sits differently around each axis, so the integral gives different values.
  2. Distance squared · The integral sums mass times distance squared.
  3. Thin hoop, mass at rim · The hoop keeps every bit at the full radius, farthest from the axis.
  4. 1 plus 3 times 1 squared, which is 4 · Add M times the squared shift to the centre value.
  5. 9 · Energy is half I omega squared.
  6. False · Among parallel axes, every shift away adds a positive correction, so I only grows when moving away.
  7. 18 · All hoop mass sits at the rim, so multiply mass by radius squared.
  8. 2MR over 3, less than the hoop · First-power weighting gives the disc 2MR over 3, not MR, so the shapes still differ.
Worksheet · LightMySky