# Worksheet: Newton's Second Law of Motion for Rotation in terms of Moment of Inertia and Angular Acceleration

In this worksheet, we will practice calculating the torque on an object given its moment of inertia and its angular acceleration.

**Q1: **

The graph shows how the angular accelerations of five objects, i–v, vary with the torque applied to them.

Which object has the greatest moment of inertia?

- Av
- Bii
- Civ
- Di
- Eiii

Which object has the smallest moment of inertia?

- Aiv
- Bi
- Cii
- Dv
- Eiii

**Q2: **

An object that is initially not rotating has a constant torque of
3.6 N⋅m
applied to it. The object has a moment of inertia of
6.0 kg⋅m^{2}.
What is the magnitude of the angular acceleration of the object?

**Q3: **

A spinning metal sphere has a moment of inertia of
1.7 kg⋅m^{2}.
It has a constant angular acceleration of
2.0 rad/s^{2}.
What is the magnitude of the torque on the object?

**Q4: **

A solid copper disk has a mass of 10 kg,
a radius of 12 cm,
and a thickness of 2.5 cm.
The disk is initially not rotating. What torque must be applied to the sphere,
about the axis around which the disk is rotationally symmetric,
to produce an angular acceleration of 0.25 rad/s^{2}?
Give your answer to 2 significant figures.

**Q5: **

Which of the lines on the graph shows how the angular acceleration of an object varies with the torque applied to it?

- AThe red line
- BThe orange line
- CThe violet line
- DThe blue line
- EThe green line

**Q6: **

The graph shows how the angular acceleration of an object varies with the torque applied to it. What is the moment of inertia of the object?

**Q7: **

An object that is initially not rotating has a torque of
30 N⋅m applied to it.
This produces an angular acceleration of
2.5 rad/s^{2}.
What is the moment of inertia of the object?

**Q8: **

In a hard disk drive, a constant torque of 14.0 N⋅m
is applied to the magnetic disk when the drive starts recording data. The magnetic disk has a moment of inertia of
1.12 kg⋅m^{2}.
What is the magnitude of the angular acceleration of the disk?

**Q9: **

The wheel of a train carriage has a moment of inertia of 28 kg⋅m^{2}.
As the train is increasing in speed as it leaves the station, the angular acceleration of the wheel is
1.5 rad/s^{2}.
What is the magnitude of the torque being applied to the wheel?

**Q10: **

Which of the following formulas correctly defines the torque, , on an object in terms of its moment of inertia, , and its angular acceleration, ?

- A
- B
- C
- D
- E

**Q11: **

A car is initially moving along a road at a constant speed. Then, the car accelerates. A torque of 21 N⋅m is applied to each of the wheels, producing an angular acceleration of 0.75 rad/s^{2} in each wheel. What is the moment of inertia of each wheel?

**Q12: **

A solid steel sphere has a mass of 8.0 kg
and a radius of 0.062 m.
The sphere is initially not rotating. What torque must be applied to the sphere to produce an angular
acceleration of 1.5 rad/s^{2}? Give your
answer to 2 significant figures.