# Rotational Motion: Flywheel

A rim type flywheel has to store the greatest amount of energy of 2.5 kJ at the mean engine speed of 300 rpm. The fluctuation of speed is not allowed to exceed 1.5% of the mean and the mass of the flywheel is 500 kg. Assuming the flywheel to be of cast iron and having its internal diameter 0.9 of its external diameter, find the diameters and the thickness of the rim. Take the density of cast iron as 7200 kg m-3.

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First we have to determine the moment of inertia of the flywheel about its axis of rotation. Let us consider a hollow cylinder of radius r and thickness dr and width same as that of the flywheel (say L), co-centric with the flywheel as shown in the fig..

Volume of the cylinder = dV = (2Пr)dr x L

Mass of the cylinder = dm = Volume x Density = (2Пr)dr x L x ρ = 2ПρL rdr

By definition moment of inertia of the ...

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