Question

A ceiling fan with 86-cm-diameter blades is turning at 70 rpm . Suppose the fan coasts to a stop 27 safter being turned off.

Part A

What is the speed of the tip of a blade 10 s after the fan is turned off?

Part B

Through how many revolutions does the fan turn while stopping?

Answer 1

initial angular velocity is wi = 70 rpm = 70*2*3.142/60 = 7.33 rad/sec

time taken to stop is t = 27 sec

final angular velocity at t = 27 sec is wf = 0 rad/sec

angular accelaration is alpha

Using wf = wi + (alpha*t)

0 = 7.33 + (alpha*27)

alpha = -0.271 rad/sec^2

then after 10 sec

angular speed is wf = wi+(alpha*t)

wf = 7.33-(0.271*10) = 4.62 rad/sec = 4.62*(60/(2*3.142)) = 44 rpm

B) using theta = (wi*t) + (0.5*alpha*t^2)

theta = (7.33*27) -(0.5*0.271*27^2) = 99.12 rad

theta = 99.12 rad = 99.12/(2*3.142) = 15.77 rev

so the no.of revolutions before stopping is 15 rev