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  4. A fly wheel is a uniform disc of mass 72 kg and radius 50 cm . When it is rotating at the rate of 70 rpm, its kinetic energy is

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Q. A fly wheel is a uniform disc of mass $72\, kg$ and radius $50\, cm .$ When it is rotating at the rate of $70 \,rpm$, its kinetic energy is

System of Particles and Rotational Motion

Solution:

Kinetic energy of flywheel,
$K =\frac{1}{2} I \omega^{2}=\frac{1}{2} \times \frac{1}{2} M R^{2} \omega^{2}=\frac{1}{4} M R^{2} \omega^{2} $
$=\frac{1}{4} \times 72\left(\frac{50}{100}\right)^{2}\left(\frac{2 \pi \times 70}{60}\right)^{2}=241.5 J \sim 242 J $.