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A circular disc is rotating about its own axis at uniform angular velocity $ω$ The disc is subjected to uniform angular retardation by which its angular velocity is decreased to $ω / 2$ during 120 rotations. The number of rotations further made by it before coming to rest is ___

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answer is 40.

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Detailed Solution

$ω^{2} - ω_{0}^{2} = 2 α θ$

$\frac{{(\frac{ω}{2})}^{2} - ω^{2} = 2 a 2 π (120)}{0 - {(\frac{ω}{2})}^{2} = 2 a 2 π N_{2}} \Rightarrow \frac{\frac{3}{4}}{\frac{1}{4}} = \frac{120}{N_{2}} \Rightarrow N_{2} = 40$

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