Question

a cooling fan is turned off when it is running at 850rev/min. it turns 1250revolution before it comes to a stop . what was the fan angular acceleration, assume constant ...How long did it take the fan to come to a complete stop​

Answer 1

Given:

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

It turns 1250 revolution before it comes to a stop.

To find:

What was the fan angular acceleration, assume constant ...How long did it take the fan to come to a complete stop​

Solution:

From given, we have,

wi = 850 rev/min

= 850 rev/min × 2π rad/1 rev × 1 min/60 s

∴ wi = 89.012 rad/s

wf = 0 rad/s

Δθ = 1250 rev

= 1250 rev × 2π rad/1 rev

∴ Δθ = 7853.975 rad

What was the fan's angular acceleration, assumed constant?

wf² = wi² + 2αΔθ

α = (wf² - wi²)/2Δθ

= (0² - 89.012²)/(2 × 7853.975)

= -0.504 rad/s²

∴ The angular acceleration α = -0.504 rad/s²

How long did it take the fan to come to a complete stop​?

wf = wi + αt

t = (wf - wi)/α

= (0 - 89.012)/(-0.504)

= 176.61 s

∴ The time taken by the fan to come to a complete stop t = 176.61 s