An airplane propeller is 2.18 m in length (from tip to tip) and has a mass of 11

Question

An airplane propeller is 2.18m  in length (from tip to tip) and has a mass of 117kg . When the airplane's engine is first started, it applies a constant torque of 1890N?m  to the propeller, which starts from rest.

part a: What is the angular acceleration of the propeller? Treat the propeller as a slender rod.  ________ rad/s

part b: What is the propeller's angular speed after making 5.00 rev? _________ rad/s

part c: How much work is done by the engine during the first 5.00 rev? ________J

part d: What is the average power output of the engine during the first 5.00 rev? ______ kW

part e:

Explanation / Answer

MOI I = (1/12)*M*L^2 = (1/12)*117*2.18^2 = 46.3359 kg m^2

T = I*alfa

a) alfa = T/I = 40.7891 rad/s^2

b) theta = 5 rev = 5*2*pi rad

alfa = Wf^2 - Wi^2 / (2*theta)

Wf =sqrt(2* alfa*theta) = sqrt(2*40.7891*5*2*3.14)

Wf = 50.6118 rad/s

c) W = 0.5*I*Wf^2 = 59345.9893 = 59346 J ...or W = Torque*theta = 59346 J

d) alfa = Wf/t ======> t = Wf/alfa = 1.2408 s

Power = W/t = 47828.8201 W = 47.828 kW

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