\[E_k = \frac{1}{2}I\omega^2\]
Variables
Ekrotational kinetic energy (J)
Imoment of inertia (kg·m²)
Omangular velocity [rad/s]
Description
What is this formula?
The rotational kinetic energy equation calculates the energy associated with the rotation of a rigid body around an axis.
When to use it
Use this formula when analyzing rotating machinery, flywheels, turbines, gears, motors, or any mechanical system involving rotational motion.
Example
A rotating disk has a moment of inertia of 12 kg·m² and angular velocity of 15 rad/s.
Data:
I = 12 kg·m²
Om = 15 rad/s
Formula:
Ek = 0.5*I*Om²
Substitution:
Ek = 0.5*12*15²
Result:
Ek = 1350 J
Applications
Mechanical engineering, rotating machinery, turbine systems, flywheel energy storage, robotics, and rotational dynamics.