Rotational kinetic energy

Definition

Rotational kinetic energy is the energy possessed by a rotating object due to its angular motion. It is given by the formula $KE_{rot} = \frac{1}{2}I\omega^2$, 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, $I$, depends on how an object's mass is distributed relative to the axis of rotation.
3. Angular velocity, $\omega$, is measured in radians per second (rad/s).
4. Rotational kinetic energy can be converted into other forms of energy, such as translational kinetic energy or potential energy.
5. In systems with both rotational and translational motion, total kinetic energy is the sum of translational kinetic energy ($KE_{trans} = \frac{1}{2}mv^2$) and rotational kinetic energy.

Review Questions

• What variables are needed to calculate rotational kinetic energy?
• How does increasing an object's moment of inertia affect its rotational kinetic energy, assuming constant angular velocity?
• Explain how rotational kinetic energy changes when an ice skater pulls their arms in during a spin.

Related terms

Moment of Inertia:

A measure of an object's resistance to changes in its rotation rate. It depends on the mass distribution relative to the axis of rotation.

$\omega$ (Angular Velocity): The rate at which an object rotates or revolves around an axis; measured in radians per second (rad/s).

$KE_{trans}$ (Translational Kinetic Energy): The energy due to linear motion, calculated as $KE_{trans} = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is linear velocity.