# Rotational Kinetic Energy Formula

Kinetic energy is the energy of moving objects, including objects that are rotating. The kinetic energy of a rotating object depends on the object's angular (rotational) velocity in radians per second, and on the object's moment of inertia. Moment of inertia is a measure of how easy it is to change the rotation of an object. Moments of inertia are represented with the letter *I*, and are expressed in units of *kg∙m ^{2}*. The unit of kinetic energy is Joules (J). In terms of other units, one Joule is equal to one kilogram meter squared per second squared ().

*K* = kinetic energy ()

*I* = moment of inertia (*kg∙m ^{2}*)

*ω* = angular velocity (radians*/s*)

Rotational Kinetic Energy Formula Questions:

1) A round mill stone with a moment of inertia of *I* = 1500 *kg∙m ^{2}* is rotating at an angular velocity of 8.00 radians

*/s*. What is the stone's rotational kinetic energy?

Answer: The rotational kinetic energy of the mill stone can be found using the formula:

K = 48 000 J

The rotational kinetic energy of the mill stone is 48 000 J.

2) What is the rotational kinetic energy of a DVD (digital video disc) with a moment of inertia of *I* = 1.000×10^{-4} *kg∙m ^{2}*, rotating at an angular velocity of 760.0 radians

*/s*?

Answer: The rotational kinetic energy of the DVD can be found using the formula:

K = 28.88 J

The kinetic energy of the rotating DVD is 28.88 J.

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