Rotational Kinetic Energy Calculator (KE = ½Iω²)
Rotational kinetic energy is the energy an object has because it is spinning. A figure skater pulling their arms in spins faster and stores more rotational energy without any external push. This calculator finds that energy from the moment of inertia and angular velocity, with built-in RPM to rad/s conversion.
How Rotational Kinetic Energy Works
The formula: KE = 1/2 I omega squared, where I is the moment of inertia (how mass is distributed around the axis) and omega is the angular velocity in radians per second.
Converting RPM to rad/s
Most real-world specs list rotation speed in RPM. To convert: omega = RPM x 2 pi / 60. A car engine at 3,000 RPM spins at about 314 rad/s.
Moment of Inertia Quick Reference
| Shape | Formula |
|---|---|
| Solid cylinder/disk | I = 1/2 mr squared |
| Hollow cylinder | I = m r squared |
| Solid sphere | I = 2/5 mr squared |
| Thin rod (center) | I = 1/12 mL squared |
Real-World Examples
- Flywheel energy storage: Industrial flywheels spin at 10,000+ RPM to store energy for grid stabilization.
- Bicycle wheel: A 1.5 kg wheel with r = 0.35 m at 200 RPM stores about 13 J of rotational energy.
- Washing machine drum: The spin cycle at 1,200 RPM uses rotational kinetic energy to extract water from clothes.