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  4. The angular velocity of a wheel increases from 100 rps to 300 rps in 10 seconds . The number of revolutions made during that time is

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Q. The angular velocity of a wheel increases from $ 100\, rps $ to $ 300 \,rps $ in $ 10\, seconds $ . The number of revolutions made during that time is

KEAMKEAM 2008System of Particles and Rotational Motion

Solution:

Angular displacement during time
$ \theta =({{\omega }_{2}}-{{\omega }_{1}})t $
$ =(2\pi {{n}_{2}}-2\pi {{n}_{1}})t $
$ =(600\pi -200\pi )\times 10 $
$ =4000\text{ }\pi \text{ }rad $
Therefore, number of revolutions made during this time $ =\frac{4000\pi }{2\pi }=2000 $