# A circular disk of uniform thickness 20 mm, radius 100 mm and mass 20 kg is used a s flywheel. If it rotates at 600 rpm, kinetic energy of flywheel is

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A circular disk of uniform thickness 20 mm, radius 100 mm and mass 20 kg is used a s flywheel. If it rotates at 600 rpm, kinetic energy of flywheel is Joule is

1. 395
2. 790
3. 1580
4. 3160

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Correct Answer - Option 1 : 395

Concept:

Flywheels

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

The kinetic energy of the flywheel can be calculated by:

$KE= \frac{1}{2}I{\omega ^2}$

where

I = moment of inertia of thin disc = mR2

ω = angular velocity of the flywheel = $\frac{{2\pi N}}{{60}}$

Calculation:

Given:

Mass of flywheel (m) = 20 kg, radius (R) = 100 mm = 0.1 m, N = 600 rpm

I = mR2

I = 20 × 0.12

I = 0.2 kg/m2

$w = \frac{{2\pi N}}{{60}} = \frac{{2~ ×~ \pi ~×~ 600}}{{60}} = 62.84\;rad/s$

∴ ${\rm{K}}.{\rm{E}} = \frac{1}{2}{\rm{I}}{{\rm{\omega }}^2} = \frac{1}{2} × 0.2 × {\left( {62.84} \right)^2} = 395{\rm{\;J}}$

Moment of inertia of a thin disc is mR2

Moment of inertia of a thick disc or flywheel is $\frac{{m{R^2}}}{2}$

Since here in the question thickness is very very less so it is a thin disc