Flywheel Calculator
A flywheel stores the fluctuation of energy ΔE = Iω²Cs: 5 kJ at 600 rpm with Cs = 2 % needs I = 63.3257 kg·m².
Cs = (Nmax − Nmin)/N; ±1 % is Cs = 2 %.
For the flywheel mass; 0 to skip.
63.3257397764611 kg·m²
Full answer, then cut to fewer decimals (not rounded):
- 63.3257397764611 kg·m²
- 63.325739776461 kg·m²
- 63.32573977646 kg·m²
- 63.3257397764 kg·m²
- 63.325739776 kg·m²
- 63.32573977 kg·m²
- 63.3257397 kg·m²
- 63.325739 kg·m²
- 63.32573 kg·m²
- 63.3257 kg·m²
- 63.325 kg·m²
- 63.32 kg·m²
- 63.3 kg·m²
- Flywheel mass m = I/k²
- 253.303 kg
- Mean angular speed ω
- 62.8319 rad/s
- Maximum speed
- 606 rpm
- Minimum speed
- 594 rpm
- Kinetic energy at mean speed ½Iω²
- 125 kJ
Step-by-step solution
- ΔE = I ω² Cs
- ω = 2πN/60 = 62.8319 rad/s
- I = ΔE ÷ (ω² Cs) = 5000 ÷ (3947.84 × 0.02) = 63.3257 kg·m²
Flywheel Formula
ΔE = I ω² Cs = m k² ω² Cs
Cs = (ωmax − ωmin)/ω, k radius of gyration
Worked Example
ΔE = 5000 J at 600 rpm with Cs = 2 % and k = 0.5 m:
- ΔE = I ω² Cs
- ω = 2πN/60 = 62.8319 rad/s
- I = ΔE ÷ (ω² Cs) = 5000 ÷ (3947.84 × 0.02) = 63.3257 kg·m²
Mean angular speed ω: 62.8319 rad/s · Maximum speed: 606 rpm · Minimum speed: 594 rpm · Kinetic energy at mean speed ½Iω²: 125 kJ
More Theory of Machines and Vibrations Calculators
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N₁/Nout = Π driven teeth ÷ Π driving teeth
train value = 1/speed ratio
Example: A compound train 20/60 then 15/45 driven at 1200 rpm: Output speed N = 133.333 rpm.
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Transmissibility Calculator
TR = √[1 + (2ζr)²] ÷ √[(1 − r²)² + (2ζr)²]
r = ω/ωn frequency ratio, ζ damping ratio
Example: A machine running at twice the natural frequency with ζ = 0.1: Transmissibility TR = 0.355862.
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Belt Tension Calculator
T₁/T₂ = e^(μθ), P = (T₁ − T₂) v
μ friction (μ/sin β for a V-belt), θ wrap angle, Tc = mv²
Example: A flat belt, Tmax = 2000 N, 0.5 kg/m, 20 m/s, μ = 0.3, θ = 165°: Power transmitted P = 20.826 kW.
Frequently asked questions
What does ±1 % speed fluctuation mean for Cs?
Cs is the total band, (Nmax − Nmin)/N, so ±1 % is Cs = 0.02.
How is ΔE found from a turning-moment diagram?
It is the largest difference between the cumulative areas above and below the mean torque line, converted to joules.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Flywheel Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/flywheel-calculator/
IEEE
Scientific Converters, "Flywheel Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/flywheel-calculator/