When a fan is turned off after having been run for a long period of time, it slo

Question

When a fan is turned off after having been run for a long period of time, it slows from 300 revolutions per minute to a stop in 40 seconds. Assume uniform angular deceleration. It is now turned back on again. The fan has four blades, each with a moment of inertia of 0.6 kg m^2 and a central hub which consists of a 6 kg disk of radius 20 cm. When the fan is turned back on, it takes 30 seconds to get back up to 300 revolutions per minute, the standard running speed. Determine the steady-state torque being provided by the motor when running at full speed. Determine the start-up torque in effect during the period the fan blades are speeding up.

Explanation / Answer

2. wi = 300 rpm = 300 x 2pi rad / 60s = 31.42 rad/s

t = 40 s

Applying wf = wi + alpha t

0 = 31.42 + 40 x alpha1

alpha1 = - 0.785 rad/s^2

I = (4 x 0.6) + (6 x 0.20^2 / 2) = 2.52 kg m^2

frictional torque = I alpha = 1.98 N m

(A) Steady state torque will be equal to frictional torque

Ans: 1.98 N m

(B) during start up

31.42 = 0 + 30 alpha2

alpha2 = 1.05 rad/s^2

net torque = 1.98 + (2.52 x 1.05) = 4.62 N m

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