Rotation Dynamics mastering physics 10.32

AI Thread Summary
To calculate the work done by the airplane propeller after 5 revolutions, the correct formula involves multiplying the torque by the total angle in radians, which is 1950 Nm multiplied by 10π radians. The initial calculation was close but needed adjustment to account for the correct angle. For average power, the formula used was torque multiplied by angular velocity, but the angular velocity needs to be accurately determined based on the propeller's rotation. The discussion highlights the importance of precise calculations in rotational dynamics to achieve correct results.
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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 1950 Nm to the propeller, which starts from rest.

How much work in joules is being done after 5 revolutions?

This is what I did: (1.04*1950)*(5*2*pi). Mastering physics says it is close, but not correct.
 
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figured that out: (1950)*(5*2pi)
Now I need to calculate the average power. power=T_z*w_z
=1950 Nm *53.9 rads/s.

mastering physics says this is incorrect. Any ideas?
 

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