A flywheel is in the form of uniform circular disc of diameter 10 cm & mass 10 kg is rotating about its own axis calculate the kinetic energy when rotating at 1200 rpm

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) = 10 kg, radius (r) = 10/2 =5 cm = 0.05 m, N = 1200 rpm

\(I = \frac{{m{R^2}}}{2} = \frac{{10 ~\times ~{{0.05}^2}}}{2} = 0.0125\;kg - {m^2}\)

\(w = \frac{{2\pi N}}{{60}} = \frac{{2~ \times~ \pi ~\times~ 1200}}{{60}} =40\pi\;rad/s\)

∴ \({\rm{K}}.{\rm{E}} = \frac{1}{2}{\rm{I}}{{\rm{\omega }}^2} = \frac{1}{2} \times 0.0125 \times {\left( {40\pi} \right)^2} = 10 \pi^2{\rm{\;J}} \)