# 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, , of a rotating object varies with the moment of inertia, , of that object around its axis of rotation?

- A
- B
- C
- D
- E

**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
m^{2} 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
m^{2} 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 , what is its angular velocity after the torque has been applied? Give your answer to 3 significant figures.

**Q5: **

Which of the following relations describes how the rotational kinetic energy, , of a rotating object varies with the angular velocity, , of that object?

- A
- B
- C
- D
- E

**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
m^{2}.
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
m^{2}.
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.