**Concept:**

Fluctuation of energy in a flywheel is given as

**ΔE = Iω**^{2}C_{s}

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 = Iω^{2}C_{s}

\(I={\Delta E \over {\omega ^2 \ C_s} }={6240 \over {83.77 ^2 \ \times \ 0.02} }\)

**I = 44.46 kg-m**^{2}