Question

A cooling fan is turned off when it is running at 900 rev/min. It turns 1700 revolutions before it comes to a stop.

(a) What was the fan's angular acceleration, assumed constant?
____rad/s2
(b) How long did it take the fan to come to a complete stop?
____s

Answer 1

a)α = - 0.415 rad/s²

b)t=226.68 sec

Step-by-step explanation:

Given

Initial angular speed

ωi= 900 rev/min

`\omega_i=(2\pi* 900)/(60)\ rad/s`

ωi= 94.24

θ = 1700 rev

We know that

1 rev = 2π rad

θ = 3400π rad

Final angular speed ωf=0 rad/s

α=Angular acceleration

We know that

ωf² = ωi²+ 2 α θ

0² = 94.24²+ 2 x 3400π x α

α = - 0.415 rad/s²

Negative sign indicates that acceleration and speed is in opposite direction.

We also know that

ωf = ωi+ α t

0 = 94.24 - 0.415 x t

t=226.68 sec

a)α = - 0.415 rad/s²

b)t=226.68 sec