Question

The blades of a fan running at low speed turn at 200 rpm. When the fan is switched to high speed, the rotation rate increases uniformly to 340 rpm in 5.92 s.

(a) What is the magnitude of the angular acceleration of the blades?

(b) How many revolutions do the blades go through while the fan is accelerating?

Answer 1

a. Vf - Vo = 340 - 200 = 140 rev/mi =
140 rev/60 s = 2.33 rev/s.

a = (Vf - Vo)/t = 2.33 rev/s / 5.92 s =
0.39 rev/s^2.

b. 2.33 rev/s * 5.92 s = 13.8 REVs.

Answer 2

For Part B, do (340+200)/2=270 rpm to find the average rpm during acceleration. Then divide this answer by 60 seconds to find the average revolutions per second during acceleration 270/60=4.5 rev/sec. Multiply this answer by the amount of seconds it takes for it to accelerate and you will have your answer 4.5*5.92=26.64 rev.