Question

When turned on, a fan requires 5.0 seconds to get up to its final operating rotational speed of 1200 rpm. a) How large is the final operating angular speed, in rad/s? b) What was the angular acceleration of the fan, in rad/s^2?

Answer 1

a)

125.6 rad/s

b)

25.12 rad/s²

Step-by-step explanation:

a)

t = time required by the fan to get up to final operating speed = 5 sec

w = final operating rotational speed = 1200 rpm

we know that :

1 revolution = 2π rad

1 min = 60 sec

w =
`1200(rev)/(min)(2\pi rad)/(1 rev)(1 min)/(60 sec)`

w =
`(1200* 2\pi )/(60)(rad)/(s)`

w = 125.6 rad/s

b)

w₀ = initial angular speed = 0 rad/s

α = angular acceleration

using the equation

w = w₀ + α t

125.6 = 0 + α (5)

α = 25.12 rad/s²