Question

A cooling fan is turned off when it is running at 850 rev/min. It turns 1250 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

Initial rotational speed of the fan = N₁ = 850 rev/min

Initial angular speed of the fan = $\omega$ ₁

W = 27 Ni 60

2 (850) = الند 60

$\omega$₁ = 89.01 rad/s

Final angular speed of the fan = $\omega$ ₂ = 0 rad/s (Comes to a stop)

Number of revolutions the fan makes before coming to a stop = n = 1250 rev

Angle through which the fan rotates before coming to a stop = $\theta$

$\theta$ = 2$\pi$n

$\theta$ = 2$\pi$(1250)

$\theta$ = 7853.98 rad

Angular acceleration of the fan = $\alpha$

$\omega$₂² = $\omega$ ₁² + 2$\alpha$$\theta$

(0)² = (89.01)² + 2$\alpha$(7853.98)

$\alpha$ = -0.5044 rad/s²

Negative as it is deceleration.

Time taken for the fan to come to a complete stop = T

$\omega$₂ = $\omega$ ₁ + $\alpha$ T

0 = 89.01 + (-0.5044)T

T = 176.5 sec

a) Angular acceleration of the fan = -0.5044 rad/s²

b) Time taken for the fan to come to a complete stop = 176.5 sec