Concept:
Fluctuation of energy in a flywheel is given as
ΔE = Iω2Cs
Where I = Mass moment of inertia; ω = Angular speed; Cs = Coefficient of fluctuation of speed;
\(C_s={(N_{max} - N_{min}) \over N}\)
\(\omega ={2\pi N \over 60}\)
Where N = Speed in rpm
Calculation:
Given:
N = 800 rpm; ΔE = 6240 J; Fluctuation of angular speed = ±1%; I = ?
\(\omega ={2\pi N \over 60}={2\pi\times800 \over 60}\) = 83.77 rad/s
\(C_s={(N_{max} - N_{min}) \over N}\)
\(C_s={(1.01\ N \ -\ 0.99\ N) \over N}\) (∵ fluctuation = ±1%)
Cs = 0.02
Now,
ΔE = Iω2Cs
\(I={\Delta E \over {\omega ^2 \ C_s} }={6240 \over {83.77 ^2 \ \times \ 0.02} }\)
I = 44.46 kg-m2