Worksheet: Newton's Second Law of Motion for Rotation in terms of Angular Momentum and Time

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, 𝜏, applied to an object in terms of the change in its angular momentum, Δ𝐿, and the time for which the torque is applied, Δ𝑡?

  • A𝜏=Δ𝐿Δ𝑡
  • B𝜏=Δ𝐿Δ𝑡
  • C𝜏=12Δ𝐿Δ𝑡
  • D𝜏=Δ𝑡Δ𝐿
  • E𝜏=Δ𝐿Δ𝑡

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 𝑡=8s?

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 𝑡=8s?

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⋅m2/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⋅m2/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⋅m2/s
  • B67 kg⋅m2/s
  • C580 kg⋅m2/s
  • D0.015 kg⋅m2/s
  • E960 kg⋅m2/s

Q7:

The wheel of a car initially has an angular momentum of 12 kg⋅m2/s. The car accelerates and a constant torque of 1.8 N⋅m is applied to the wheel for 15 s. What is the angular momentum of the wheel after the car’s acceleration?

Q8:

A spinning metal disk initially has an angular momentum of 2.4 kg⋅m2/s. A constant torque is applied to the disk. Over a time of 4.0 s, its angular momentum increases to 3.6 kg⋅m2/s. What is the magnitude of the torque that is applied to the disk?

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 𝑡=8s?

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 0.060 kg⋅m2/s. For how long has the torque been applied to the ball?

Q11:

The graph shows the angular momentum of an object over time. The object initially has an angular momentum of zero. From 𝑡=0s to 𝑡=3s, a torque is applied to the object.

What is the magnitude of the torque?

Q12:

A footballer kicks a football off the ground, giving the football both linear momentum and angular momentum. The angular momentum of the football increases by 0.56 kg⋅m2/s in just 0.020 s. What is the magnitude of the average torque applied to the football?

Q13:

The graph shows the angular momentum of an object over time. The object initially has an angular momentum of zero. Between 𝑡=0s and 𝑡=6s, two torques of different magnitudes are applied to the object.

What is the average torque applied to the object over this time?

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