A propeller consists of three identical blades each with a mass of 5.8 kg and a

Question

A propeller consists of three identical blades each with a mass of 5.8 kg and a length of 0.52 m that are attached to a central hub with a diameter of 0.16 m. The propeller is spinning at a rate of 65 rad/s when a brake is applied to the outer surface of the hub that brings it to a stop in 16 s.

a) What is the rotational inertia of the propeller? (assume that the mass of the hub is negligible compared to the blades)
b) What is the angular acceleration of the brake on the propeller?
c) What is the torque provided by the brake?
d) What is the average force exerted by the brake?

Explanation / Answer

mass of the blade m = 5.8 kg length of the blade l = 0.52 m diameter of the hub d = 0.16 m angular velocity of the propeller ? = 65 rad/sec time taken to stop = 16 secnext step (a) given three blades are identical. Inertial of the blade = 1/3(ML^2) = 1/3(5.8*(0.52)^2) = 0.52 kg-m rotational Inertia of the total propeller(I) = 3*0.52 = 1.56 kg-m....(1) (b) angular acceleration(a) = d?/dt = 0-65/16-0 = -4.0625 rad/sec^2 ......(2) here negative sign represents the retardation of the propeller with time. (c) Torque t = Ia = (1.56)*(4.0625) = 6.33 N.m (d) force F = I?/t = 65*1.56/16 = 6.33 N

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