Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 4 / 11C / b / iii

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- Solution iii

Solution

The work law means that friction exerts a constant opposing torque of magnitude

W

. Until the cone stops,

I \overset{ω}{˙} = - W .

Its initial angular speed is

ω_{0} = 2 K_{0} / I

, and uniform angular deceleration gives

0 = ω_{0} - \frac{W}{I} t .

Therefore

t = \frac{I ω _{0}}{W} = \frac{2 K _{0} I}{W ^{2}} .

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