Rotational Kinetic Energy Calculator
Calculate the kinetic energy of a rotating object from its moment of inertia and angular velocity.
Compare to translational kinetic energy.
A rotating object has kinetic energy stored in its rotational motion:
E_rot = ½Iω²
Where:
- E_rot = Rotational kinetic energy (joules, J)
- I = Moment of inertia (kg·m²)
- ω = Angular velocity (radians per second, rad/s)
Converting RPM to rad/s: ω = RPM × 2π / 60
Total kinetic energy of a rolling object: An object that rolls (like a wheel) has both translational and rotational kinetic energy: E_total = ½mv² + ½Iω² = ½mv²(1 + I/(mR²))
For a solid disk rolling without slipping: E_total = ½mv² + ½(½mR²)(v/R)² = ¾mv²
Why rotational KE matters:
Flywheels store energy as rotational kinetic energy. A 100 kg steel flywheel with R = 0.5 m (I = ½MR² = 12.5 kg·m²) spinning at 3000 RPM (ω = 314 rad/s): E = ½ × 12.5 × 314² ≈ 617,000 J ≈ 617 kJ
This is why flywheels are used in:
- Engines: to smooth out power strokes
- Electric grids: flywheel energy storage for frequency regulation
- Formula 1 cars: KERS (kinetic energy recovery system) stores braking energy in a flywheel
- Buses: some city buses use flywheel energy storage instead of batteries