# An engine, connected with a flywheel, is designed to operate at an average angular speed of 800 rpm. During operation of the engine, the maximum chang

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An engine, connected with a flywheel, is designed to operate at an average angular speed of 800 rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to be 6240 J. In order to keep the fluctuation of the angular speed within ±1% of its average value, the moment of inertia (in kg-m2) of the flywheel should be ____________.

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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

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