Angular velocity of airplane propeller

AI Thread Summary
The discussion revolves around calculating the angular acceleration and angular speed of an airplane propeller given its dimensions and the applied torque. The angular acceleration is determined to be 46.23 rad/s² using the formula I=(1/12)ML² and the relationship between torque and angular acceleration. For finding the angular speed after 5 revolutions, confusion arises regarding the correct formula to use. The hint suggests employing a method similar to constant linear acceleration problems, emphasizing the need to calculate time based on angular displacement before finding angular speed. The discussion highlights the importance of applying analogous principles from linear motion to rotational motion.
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here is the problem:
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 N*m to the propeller, which starts from rest.
-What is the angular acceleration of the propeller? Treat the propeller as a slender rod.
For this part i got 46.23 rad/s^2 finding first I=(1/12)ML^2
and then plugging that into acc angular = torque/I

What is the propeller's angular speed after making 5.00 rev?
-for this part i get confused, am i supposed to use
5 rev "per min". i used the formula v = w*r where
w= 2*pi*frequency, but it is not right.
can anyone direct me to the right formula??
thanks.
 
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Hint

Remember the problems you have solved with constant linear acceleration g? In that case, if you were asked how fast an object was moving after it had gone a certain distance, you would first use the fact that x=(1/2)gt^2 (if initial position is zero and initial velocity is zero) to solve for t, given some position x. Then you would substitute that value of t into v=gt, and you would have your answer.

The angular acceleration procedure is very much analogous.
 
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