Rotational kinetic energy

Definition

Rotational kinetic energy is the energy an object possesses due to its rotation. It is given by $$KE_{rot} = \frac{1}{2} I \omega^2$$, where $I$ is the moment of inertia and $\omega$ is the angular velocity.

5 Must Know Facts For Your Next Test

1. Rotational kinetic energy depends on both the moment of inertia and the square of the angular velocity.
2. The moment of inertia is a measure of an object's resistance to changes in its rotational motion.
3. An object with a larger moment of inertia will have more rotational kinetic energy for a given angular velocity.
4. Rotational kinetic energy can be converted to other forms of energy, such as translational kinetic energy or potential energy, depending on the system.
5. In systems involving both translational and rotational motion, the total kinetic energy is the sum of translational and rotational kinetic energies.

Review Questions

• How does increasing the angular velocity affect the rotational kinetic energy?
• What role does the moment of inertia play in determining rotational kinetic energy?
• Is it possible for two objects with different moments of inertia to have the same rotational kinetic energy? Explain.

Related terms

Moment of Inertia:

A scalar quantity that measures how much torque is needed for a desired angular acceleration about a rotational axis; it depends on mass distribution relative to that axis.

Angular Velocity:

A vector quantity that represents how fast an object rotates or revolves relative to another point; measured in radians per second ($rad/s$).

Translational Kinetic Energy:

$KE_{trans} = \frac{1}{2} mv^2$, where $m$ is mass and $v$ is linear velocity; it represents the energy due to linear motion.