Question

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s. It is then turned off and coasts to a stop in an additional 40 s. The ratio of the average angular acceleration for the first 20 s to that for the last 40 s is which of the following?

a.2
b.-0.5
c.0.5
d.-2

Answer 1

option D

Step-by-step explanation:

given,

angular speed of the fan = 120 rev/min

time = 20 sec

After 40 s fan comes to rest

ration angular acceleration of the first 20 s to last 40 s.

angular acceleration for first 20 s

`\alpha_1= (\Delta \omega)/(t)`

`\alpha_1= (120)/(20)`

`\alpha_1=6 rev/s^2`

for last 40 s

`\alpha_2= (\Delta \omega)/(t)`

`\alpha_2= (0-120)/(40)`

`\alpha_2= -3 rev/s^2`

now, ratio

`(\alpha_1)/(\alpha_2)=(6)/(-3)`

`(\alpha_1)/(\alpha_2)=-2`

hence, the correct answer is option D