Worksheet: Rotational Kinetic Energy

In this worksheet, we will practice calculating the rotational kinetic energy of a rotating object from its moment of inertia and its angular velocity.

Q1:

Which of the following relations describes how the rotational kinetic energy, š¾ , of a rotating object varies with the moment of inertia, š¼ , of that object around its axis of rotation?

  • A š¾ āˆ š¼ ļŠ©
  • B š¾ āˆ 1 š¼
  • C š¾ āˆ š¼ ļŠØ
  • D š¾ āˆ š¼
  • E š¾ āˆ 1 š¼ ļŠØ

Q2:

A solid metal disk is rotating with an angular velocity of 15 rad/s. The disk has a moment of inertia of 4.0 kgā‹…m2 around its axis of rotation. What is the rotational kinetic energy of the disk?

Q3:

A football is rotating with an angular velocity of 28 rad/s. The football has a moment of inertia of 1.9 kgā‹…m2 around its axis of rotation. What is the rotational kinetic energy of the football? Give your answer to 2 significant figures.

Q4:

A rotating object has rotational kinetic energy of 4,000 J. A torque is applied to the object and 2,600 J of rotational work is done accelerating the object. If the object has a moment of inertia of 1 2 . 0 ā‹… k g m ļŠØ , what is its angular velocity after the torque has been applied? Give your answer to 3 significant figures.

  • A 20.8 rad/s
  • B 15.3 rad/s
  • C 33.2 rad/s
  • D 25.8 rad/s
  • E 23.6 rad/s

Q5:

Which of the following relations describes how the rotational kinetic energy, š¾ , of a rotating object varies with the angular velocity, šœ” , of that object?

  • A š¾ āˆ 1 šœ”
  • B š¾ āˆ šœ”
  • C š¾ āˆ šœ” ļŠØ
  • D š¾ āˆ 1 šœ” ļŠØ
  • E š¾ āˆ šœ” ļŠ©

Q6:

An object has a rotational kinetic energy of 11,250 J. Its moment of inertia around its axis of rotation is 4.0 kgā‹…m2. What is its angular velocity?

Q7:

A tennis ball has a rotational kinetic energy of 248 J. Its moment of inertia around its axis of rotation is 0.22 kgā‹…m2. What is the angular velocity of the tennis ball? Give your answer to 2 significant figures.

Q8:

An object has a rotational kinetic energy of 3,300 J and an angular velocity of 25.0 rad/s. What is the moment of inertia of the object around its axis of rotation? Give your answer to 3 significant figures.

Q9:

A baseball bat that is being swung to hit a baseball has rotational kinetic energy of 1,490 J and an angular velocity of 12.1 rad/s. What is the moment of inertia of the object around its axis of rotation? Give your answer to 3 significant figures.

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