# Rotational Kinetic Energy

on . Posted in Kinematics

Rotational kinetic energy, abbreviated as $$KE_r$$, is the energy associated with the rotational motion of an object.  Just as translational kinetic energy is the energy of an object in linear motion, rotational kinetic energy is the energy of an object in rotational motion around an axis.  It's a fundamental concept in physics and mechanics, and it helps describe the energy stored in rotating objects.

Angular velocity is a measure of how quickly the object is rotating, and it is given in units of radians per second.  The moment of inertia quantifies an object's resistance to rotational motion and depends on its mass distribution relative to the axis of rotation.

The relationship between translational kinetic energy and rotational kinetic energy is essential when considering objects with both linear and rotational motion.  For example, a rolling ball has both translational and rotational kinetic energies due to its motion.  In many mechanical systems, energy can be transferred between translational and rotational kinetic energies.  For instance, when a spinning top slows down and eventually comes to a stop, its rotational kinetic energy is converted into other forms of energy (such as heat) due to friction.

Rotational kinetic energy is relevant in various contexts, including the analysis of rotating machinery, vehicles with spinning wheels, and the behavior of objects like spinning tops and flywheels.  It provides insights into how energy is distributed and transformed in objects with rotational motion.

### Rotational Kinetic Energy formula

$$KE_r \;=\; \frac {1}{2}\; I \; \omega^2$$     (Rotational Kinetic Energy)

$$I \;=\; (2 \; KE_r) \;/\; \omega^2$$

$$\omega \;=\; \sqrt{ 2 \; KE_r \;/\; I }$$

Symbol English Metric
$$KE_r$$ = rotational kinetic energy $$lbf-ft$$ $$J$$
$$I$$ = moment of inertia $$in^4$$ $$mm^4$$
$$\omega$$  (Greek symbol omega) = angular velocity $$deg\;/\;sec$$ $$rad\;/\;s$$