# Lesson Worksheet: Moment of Inertia Physics • 9th Grade

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 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

**Q2: **

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

- Akg
^{2}⋅m^{2} - Bkg/m
^{2} - Ckg
^{2}⋅m - Dkg⋅m
^{2} - 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?

**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}

**Q5: **

A point object with a mass of 15 µg can move around a circular track that has a radius of 25 cm. What is the moment of inertia of the object around the centre of the track?

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

**Q6: **

Consider two cuboids. Each can be rotated around its center of mass, as shown in the diagram. The cuboids have the same mass and the same moment of inertia as each other. Which of the following is a true statement comparing the lengths of the cuboids, and , to their widths, and ?

- A
- B
- C
- D
- E

**Q7: **

The objects shown in the diagram rotate around the same axis and have the same moment of inertia and the same radius. What is the ratio of the mass of the hollow sphere to the mass of the solid sphere?

**Q8: **

The objects shown in the diagram both rotate around the same axis and have the same moment of inertia. The radius of both objects, , is 25 cm. What is the ratio of the mass of the thin hoop to the mass of the disk?

**Q9: **

The objects shown in the diagram rotate around the same axis and have the same moment of inertia. The radius of the disk, , equals the outer radius of the ring, . The inner radius of the ring, , is of the ring’s outer radius. What is the ratio of the mass of the disk to the mass of the ring? Answer to two significant figures.

**Q10: **

The objects shown in the diagram both rotate around the same axis and have the same moment of inertia. The radius of both objects is the same. What is the ratio of the mass of the disk to the mass of the hoop?