# 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/m
^{2} - B
kg
^{2}⋅m - C
kg⋅m
^{2} - D
- E
kg
^{2}⋅m^{2}

**Q2: **

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

- A
- B
- C
- D
- E

**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⋅m
^{2} - B
0.264 kg⋅m
^{2} - C
0.500 kg⋅m
^{2} - D
2.00 kg⋅m
^{2} - E
0.586 kg⋅m
^{2}

**Q4: **

Earth has a mass of 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
kg⋅m
^{2} - B
kg⋅m
^{2} - C
kg⋅m
^{2} - D
kg⋅m
^{2} - E
kg⋅m
^{2}

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

- A
kg⋅m
^{2} - B
kg⋅m
^{2} - C
kg⋅m
^{2} - D
kg⋅m
^{2} - E
kg⋅m
^{2}