How to use it
- Pick the shape, or “Known moment of inertia” to type I directly.
- Enter the mass and the radius (or the rod length), and the units.
- Enter the rotation speed in rad/s, rpm or revolutions per second.
Formulas
- Energy: E = ½ I ω². Angular momentum: L = I ω.
- Moments of inertia: solid disk ½mr², thin ring mr², solid sphere ⅖mr², thin shell ⅔mr², rod about its centre mL²/12, rod about one end mL²/3.
- Speed: ω = rpm × 2π ÷ 60; 1 Wh = 3600 J.
Worked example
A steel flywheel, a solid disk of 10 kg and 30 cm radius, spins at 3000 rpm. I = ½ × 10 × 0.3² = 0.45 kg·m², ω = 314.1593 rad/s, and E = ½ × 0.45 × 314.1593² = 22,206.6099 J, about 22.2 kJ or 6.1685 Wh. Its angular momentum is 141.3717 kg·m²/s.
A 5 kg solid ball of 10 cm radius turning once per second (60 rpm): I = 0.4 × 5 × 0.1² = 0.02 kg·m², E = ½ × 0.02 × (2π)² = 0.3948 J.
Tips
- Speed counts twice. Energy grows with the square of ω, so doubling the rpm stores four times the energy.
- Mind the radius unit. 30 cm entered as 30 m gives an answer 10,000 times too large.
- Real flywheels are often a rim plus a hub; add the moments of inertia of the parts and use “Known moment of inertia”.