Rotational Kinetic Energy Calculator

How Rotational Kinetic Energy Is Calculated

A spinning object stores energy in its rotation. Rotational kinetic energy is analogous to linear kinetic energy, but replaces mass with moment of inertia and velocity with angular velocity.

Rotational Kinetic Energy Formula: KE_rot = 0.5 × I × ω²

Where:

• KE_rot = rotational kinetic energy in Joules
• I = moment of inertia in kg·m²
• ω (omega) = angular velocity in radians per second

Converting RPM to rad/s: ω = RPM × 2π / 60

Common Moment of Inertia Formulas:

• Solid disk/cylinder (axis through center): I = 0.5 × m × r²
• Hollow cylinder: I = m × r²
• Solid sphere: I = 0.4 × m × r²
• Thin rod (center axis): I = (1/12) × m × L²

Worked Example: A flywheel: solid disk, mass = 20 kg, radius = 0.3 m, spinning at 3,000 RPM:

• I = 0.5 × 20 × (0.3)² = 0.5 × 20 × 0.09 = 0.9 kg·m²
• ω = 3000 × 2π / 60 = 314.16 rad/s
• KE = 0.5 × 0.9 × (314.16)² = 0.45 × 98,696 = 44,413 J ≈ 44.4 kJ

Applications:

• Flywheels store energy to smooth engine pulses in vehicles
• Gyroscopes in spacecraft use rotational inertia for attitude control
• Pottery wheels, grinding wheels, wind turbine rotors all store significant rotational KE
• Electric regenerative braking converts rotational KE back to electrical energy