First slide

Circular motion

Question

The motor of an engine is rotating about its axis with an angular velocity of 100 rev min^-1. It come to rest in 15s, after being switched off. Assuming constant angular deceleration. What are the number of revolutions made by it before coming to rest?

Moderate

A

15.6
B

32.6
C

12.5
D

40

Solution

As $ω_{f} = ω_{i} + αt$
Here, ${0=ω}_{0} - αt$
$∴ α = \frac{ω_{0}}{t} = \frac{(100 \times 2 π) / 60}{15} = 0 .7 {rads}^{- 2}$
Angle rotated before coming to rest,
$\begin{array}{l} θ = \frac{ω_{0}^{2}}{2 α} \\ θ = \frac{{(\frac{100 \times 2 π}{60})}^{2}}{2 \times 0 .7} = 78 .33 rad \end{array}$
Hence, number of rotations, $n = \frac{θ}{2 π} = \frac{78 .33}{2 π} = 12 .5$

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