An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airplane’s engine is first started, it applies a constant torque of 1952 N · m to the propeller, which starts from rest. (a) What is the angular acceleration of the propeller? Model the propeller as a slender rod and see Table 9.2. (b) What is the propeller’s angular speed after making 5.00 revolutions? (c) How much work is done by the engine during the first 5.00 revolutions? (d) What is the average power output of the engine during the first 5.00 revolutions? (e) What is the instantaneous power output of the motor at the instant that the propeller has turned through 5.00 revolutions?
Solution 34E Step 1: Given data: Constant torque = 1952 N/m Length of airplane propeller from tip to tip l = 2.08 m Mass of propeller M = 117 kg Step 2: Torque is given by = I 2 Moment of inertia of propeller is given by I = 1/12 ML 2 I = 1/12 (117 kg)(2.08 m) 2 I = 42.18 kg/m Step 3: (a).Angular acceleration of the propeller is given by = /I 2 = (1952 N/m)/(42.18 kg/m ) 2 = 46.27 rad/s Step 4: (b).The propeller angular speed after making 5.00 revolution is given by 2 w = w +02 Where = 2 5.0* radand w = 0 0 w = 2 w = 2(46.27 rad/s )(2 5*00 rad) w = 53.91 rad/sec