Question

A cooling fan is turned off when it is running at 850 rev/min. It turns 1500 revolutions before it comes to a stop. (a) What was the fan's angular acceleration, assumed constant? (b) How long did it take the fan to come to a complete stop?

Answer 1

Answer

given,

cooling fan revolution = 850 rev/min

fan turns before revolution = 1500 revolutions

$\omega = 850 \dfrac{2\pi}{60}$

$\omega = 89\ rad/s$

θ = 1500 revolution

θ = 1500 x 2 x π

θ = 9424.78 rad

a) using equation of rotation

ω² = ω₀² + 2 α θ

ω = 0 because body comes to rest

0 = 89² + 2 x α x 9424.78

α = -0.42 rad/s²

b) time take for the fan to stop

ω = ω₀ + α t

0 = 89 - 0.42 t

$t = \dfrac{89}{0.42}$

t = 211.9 s