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### Course: Mechanics (Essentials) - Class 11th>Unit 12

Lesson 5: Kinetic energy of a merry-go-round

# Rotational kinetic energy review

Overview of key terms, equations, and skills related to rotational kinetic energy, including the difference between rotational and translational kinetic energy.

## Key terms

Term (symbol)Meaning
Rotational kinetic energy (K)Kinetic energy due to rotational motion. Scalar quantity with SI units of Joules ($\text{J}$).

## Equations

EquationSymbolsMeaning in words
$K=\frac{1}{2}I{\omega }^{2}$$K$ is rotational kinetic energy, $I$ is rotational inertia, and $\omega$ is angular velocityRotational kinetic energy is directly proportional to the rotational inertia and the square of the magnitude of the angular velocity.

## Common mistakes and misconceptions

Sometimes people forget that objects can have both rotational kinetic energy and translational (linear) kinetic energy. For example, a ball that is dropped only has translational kinetic energy. However, a ball that rolls down a ramp rotates as it travels downward. The ball has rotational kinetic energy from the rotation about its axis and translational kinetic energy from its translational motion.

For deeper explanations on this topic, see our video on rotational kinetic energy.
To check your understanding and work toward mastering these concepts, check out our exercise on comparing rotational kinetic energy for different objects.

## Want to join the conversation?

• What is the total energy of a ball rolling in the air at its maximum height?
• Are the units of linear kinetic energy the same as rotational kinetic energy?
• Yes, they are the same, they are both in units of Joules which is newtons times meters since it is the amount of energy needed to exert a force a meter. Any measurement of energy are in units of Joules.
• If I have three identical disks (same m and r), one on top of the other, rotating about a central axis, will the Inertia of the system be the 3 * the Inertia of one of the disks?
• Yes it will. The inertia of a system is equal to the sum of the individual inertias. So, if all three disks have identical inertias, then the inertia of the system has to be three times the inertia of one disk.
• For rotational Kinetic energy, it's says were using Joules which is J. Why would we use Joules when the equations doesn't say anything about using Joules
(1 vote)
• Because the units used to measure Kinetic Energy are in Joules (J)