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The angular velocity of a gear is controlled according to $ω = 12 - 3 t^{2}$ where $ω$ , in radian per second, is positive in the clockwise sense and t is the time in seconds. Find the number of revolutions N through which the gear turns during the $3 s$ .

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(1) 2.73

(2) 2.58

(4) 1.23

(3) 1.43

answer is C.

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Detailed Solution

$θ = \int_{0}^{3} ωdt = \int_{0}^{3} (12 - 3 t^{2}) dt = 36 - 27 = 9 rad N = \frac{θ}{2 π} = \frac{9}{2 \times 3.14} = 1.43$

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