# Lesson Worksheet: Newton’s Second Law of Motion for Rotation in terms of Angular Momentum and Time Physics

In this worksheet, we will practice calculating the torque on an object given the change in its angular momentum over a given time interval.

**Q1: **

Which of the following formulas correctly defines the torque, , applied to an object in terms of the change in its angular momentum, , and the time for which the torque is applied, ?

- A
- B
- C
- D
- E

**Q2: **

The graph shows the torque applied to an object over time. Initially, the object has an angular momentum of zero. What is the angular momentum of the object by time ?

**Q3: **

The graph shows the torque applied to an object over time. The object initially has an angular momentum of zero. What is the angular momentum of the object by time ?

**Q4: **

For how long must a torque of 2.5 N⋅m
be applied to an object for it to gain an angular momentum of
75 kg⋅m^{2}/s?

- A 190 s
- B 30 s
- C 0.033 s
- D 73 s
- E 78 s

**Q5: **

A constant torque of 0.75 N⋅m is applied to a metal disk for
4.0 s,
after which time the disk has an angular momentum of 8.0 kg⋅m^{2}/s.
What was the angular momentum of the disk before the torque was applied?

**Q6: **

A torque with a constant magnitude of 40 N⋅m is applied to a solid sphere for 0.60 s. How much change occurs to the angular momentum of the sphere?

- A24 kg⋅m
^{2}/s - B67 kg⋅m
^{2}/s - C580 kg⋅m
^{2}/s - D0.015 kg⋅m
^{2}/s - E960 kg⋅m
^{2}/s

**Q9: **

The graph shows the torque applied to an object over time. The object initially has an angular momentum of zero. What is the angular momentum of the object by time ?

**Q10: **

A tennis ball is hit in a way that gives it both linear
and angular momentum. An average torque of
1.2 N⋅m is applied to the ball,
increasing the ball’s angular momentum by
0.06 kg⋅m^{2}/s.
For how long has the torque been applied to the ball?