Physics overview
What is rotational kinetic energy?
Rotational kinetic energy is the energy stored in a rotating object. It depends on the object's moment of inertia and angular velocity.
Formula
Rotational kinetic energy formula
Rotational Kinetic EnergyKErot = ½Iω²
- KErot is rotational kinetic energy in joules.
- I is moment of inertia in kilogram square meters.
- ω is angular velocity in radians per second.
Worked example
A rotating object has I = 4 kg·m² and ω = 3 rad/s
- Write the formula: KErot = ½Iω².
- Substitute the values: KErot = ½ × 4 × 3².
- Square angular velocity: 3² = 9.
- Calculate the energy: KErot = 18 J.
Rearranged equations
Solve for moment of inertia or angular velocity
Moment of inertia
I = 2KErot ÷ ω²
Double the rotational kinetic energy and divide by angular velocity squared.
Angular velocity
ω = √(2KErot ÷ I)
Divide twice the energy by moment of inertia, then take the square root.
Rotational resistance
Why moment of inertia matters
Moment of inertia depends on both mass and how that mass is distributed around the axis of rotation. Moving mass farther from the axis generally increases moment of inertia.
Squared relationship
Angular velocity has a large effect
Rotational kinetic energy increases with the square of angular velocity. Doubling angular velocity increases rotational kinetic energy by a factor of four when moment of inertia stays constant.
Units
Standard SI units
Use joules for rotational kinetic energy, kilogram square meters for moment of inertia, and radians per second for angular velocity.
Real-world applications
Where rotational kinetic energy is used
- Flywheels and energy-storage systems.
- Wheels, gears, and rotating shafts.
- Turbines and electric motors.
- Rotating laboratory equipment.
- Planetary and satellite rotation.
Calculation limits
Important assumptions
- All entered values must be greater than zero.
- Moment of inertia is assumed to be known for the selected axis.
- Angular velocity must be expressed consistently.
- Energy losses from friction are not included.
- Units are not converted automatically.
Related tools
Continue your rotational-motion analysis
Use the Angular Velocity Calculator to calculate angular velocity, angular displacement, or time.
Use the Kinetic Energy Calculator to calculate translational kinetic energy from mass and velocity.
Questions and answers
Rotational kinetic energy FAQ
What formula does the rotational kinetic energy calculator use?
It uses KErot = ½Iω², where rotational kinetic energy depends on moment of inertia and the square of angular velocity.
What is rotational kinetic energy?
Rotational kinetic energy is the energy an object has because it is rotating.
What is moment of inertia?
Moment of inertia measures how strongly an object resists changes in rotational motion.
How do you calculate angular velocity from rotational kinetic energy?
Use ω = √(2KErot ÷ I), where KErot is rotational kinetic energy and I is moment of inertia.