Worksheet: Moment of Inertia

In this worksheet, we will practice calculating the angular mass, called the moment of inertia, of rotating objects of various regular shapes.

Q1:

Which of the following correctly shows the SI unit for the moment of inertia?

  • A kg/m2
  • B kg2⋅m
  • C kg⋅m2
  • D ( ) k g m
  • E kg2⋅m2

Q2:

Which of the following formulas correctly relates the moment of inertia of an object, 𝐼 , to the mass of the object, 𝑚 , and the distance of the object from the axis around which it rotates, 𝑑 ?

  • A 𝐼 = 𝑚 𝑑
  • B 𝐼 = 𝑚 𝑑
  • C 𝐼 = 𝑚 𝑑
  • D 𝐼 = 𝑚 𝑑
  • E 𝐼 = 𝑚 𝑑

Q3:

A thin hoop has a radius of 1.25 m and a mass of 750 g. The hoop can rotate around an axis that intersects the hoop at the points A and B, as shown by the blue arrow in the diagram. The hoop can also rotate around an axis that intersects the midpoint of the line from A to B and does not intersect the hoop, as shown by the orange arrow. What is the difference in the moment of inertia of the hoop around these two axes?

  • A 0.413 kg⋅m2
  • B 0.264 kg⋅m2
  • C 0.500 kg⋅m2
  • D 2.00 kg⋅m2
  • E 0.586 kg⋅m2

Q4:

Earth has a mass of 5 . 9 7 × 1 0 kg and a radius of 6,370 km.

If Earth is assumed to be a solid sphere of uniform density, what is its moment of inertia?

  • A 2 . 4 2 × 1 0 kg⋅m2
  • B 1 . 9 4 × 1 0 kg⋅m2
  • C 3 . 0 4 × 1 0 kg⋅m2
  • D 3 . 2 3 × 1 0 kg⋅m2
  • E 9 . 6 9 × 1 0 kg⋅m2

If Earth was a disk, what would its moment of inertia be?

  • A 2 . 4 2 × 1 0 kg⋅m2
  • B 5 . 4 1 × 1 0 kg⋅m2
  • C 4 . 8 4 × 1 0 kg⋅m2
  • D 1 . 9 0 × 1 0 kg⋅m2
  • E 1 . 2 1 × 1 0 kg⋅m2

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