Worksheet: Angular Momentum in Terms of Moment of Inertia

In this worksheet, we will practice calculating the angular momentum of an object that is rotating from its moment of inertia.

Q1:

If the angular speed of a rotating object increases by a factor of 3, by what factor does the angular momentum of the object change?

Q2:

An object spinning with an angular speed of 20𝜋 rad/s has an angular momentum of 9𝜋 kg⋅m2/s. What is the moment of inertia of the object about its axis of rotation?

Q3:

A hollow metal sphere has a moment of inertia about its axis of rotation of 0.45 kg⋅m2 and an angular momentum of 0.79 kg⋅m2/s. How long does it take for the sphere to make one full rotation? Give your answer to 2 significant figures.

Q4:

The wheel of a car has a moment of inertia of 2.25 kg⋅m2 about its axis of rotation. As the car is driven along a road, the wheel has an angular momentum of 70.7 kg⋅m2/s. With what angular speed is the wheel rotating?

Q5:

An asteroid has a moment of inertia about its axis of rotation of 1.9×10 kg⋅m2. The asteroid makes one full rotation every 250 s. What is the angular momentum of the asteroid? Give your answer to 2 significant figures.

  • A4.8×10 kg⋅m2/s
  • B7.6×10 kg⋅m2/s
  • C3.0×10 kg⋅m2/s
  • D3.0×10 kg⋅m2/s
  • E4.8×10 kg⋅m2/s

Q6:

A solid metal sphere is rotating with an angular speed of 12.6 rad/s. It has a moment of inertia of 0.0200 kg⋅m2. What is the angular momentum of the sphere?

Q7:

The wheel of a car has a moment of inertia of 2.25 kg⋅m2 about its axis of rotation. If the wheel makes 8 turns in 1 second, what is the angular momentum of the wheel? Give your answer to 3 significant figures.

Q8:

A solid metal disk has a moment of inertia of 0.025 kg⋅m2 about its axis of rotation and has an angular momentum of 14 kg⋅m2/s. With what angular speed is the disk rotating?

Q9:

An object has a moment of inertia of 0.50 kg⋅m2 about its axis of rotation and an angular momentum of 130 kg⋅m2/s. How many times does the object rotate in 1 second? Give your answer to 2 significant figures.

Q10:

A stick being spun about its center has an angular momentum of 0.320 kg⋅m2/s. The stick is being spun at an angular speed of 25.1 rad/s. What is the moment of inertia of the stick about its axis of rotation?

Q11:

Earth has a moment of inertia about its axis of rotation of 9.69×10 kg⋅m2 and an angular speed of 7.29×10 rad/s. What is the angular momentum of Earth due to its rotation?

  • A6.65×10 kg⋅m2/s
  • B3.53×10 kg⋅m2/s
  • C1.33×10 kg⋅m2/s
  • D5.15×10 kg⋅m2/s
  • E7.06×10 kg⋅m2/s

Q12:

The magnetic disk in a hard disk drive is spinning with an angular speed of 100𝜋 rad/s. The magnetic disk has a moment of inertia of 0.00049 kg⋅m2/s. What is the angular momentum of the disk?

Q13:

The SI unit of angular momentum is kilogram - square meters per second (kg⋅m2/s). The SI unit of moment of inertia is kilogram - square meters (kg⋅m2). If angular momentum is divided by moment of inertia, what is the SI unit of the resultant quantity?

  • As−1
  • Bs−2
  • Cs
  • Dkg/s
  • Em/s

Q14:

The SI unit of angular momentum is kilogram - square meters per second (kg⋅m2/s). If angular momentum is divided by frequency, what is the SI unit of the resultant quantity?

  • Akg⋅m⋅s
  • Bkg⋅m/s
  • Ckg⋅m2
  • Dkg⋅m2⋅s
  • Ekg⋅m2/s

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