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A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as flywheel. If it rotates at 600 rpm, the kinetic energy of the flywheel, in joules is
1. 395
2. 790
3. 1580
4. 3160

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Correct Answer - Option 2 : 790

Concept:

Flywheel

 A flywheel is used to control the variation in speed during each cycle of the engine.

The kinetic energy of flywheel can be calculated by:

K.E \(= \frac{1}{2}I{w^2}\)

where I = moment of inertia of the flywheel, ω = angular velocity of the flywheel

Calculation:

Given:

Mass of flywheel (m) = 20 kg, radius (r) = 200 mm = 0.2 m, N = 600 rpm

\(I = \frac{{m{R^2}}}{2} = \frac{{20 ~\times ~{{0.2}^2}}}{2} = 0.4\;kg - {m^2}\)

\(w = \frac{{2\pi N}}{{60}} = \frac{{2~ \times~ \pi ~\times~ 600}}{{60}} = 62.83\;rad/s\)

∴ \({\rm{K}}.{\rm{E}} = \frac{1}{2}{\rm{I}}{{\rm{\omega }}^2} = \frac{1}{2} \times 0.4 \times {\left( {62.83} \right)^2} = 789.5{\rm{\;J}} \simeq 790{\rm{\;J}}\)

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