Airplane Propeller: Rotational Kinetic Energy & Angular Speed

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SUMMARY

The discussion centers on calculating the rotational kinetic energy of an airplane propeller modeled as a slender rod, with a length of 1.85 m and an original mass of 97.0 kg, rotating at 2300 rpm. The inertia is calculated using the formula I = 1/12ML^2, yielding a value of 165.99 kg·m². The kinetic energy is derived from K = 1/2Iω², resulting in a value of 4.81 x 10^6 J. When reducing the mass to 75% of its original weight, the new angular speed required to maintain the same kinetic energy is calculated to be 112592 rpm, which is deemed unrealistic.

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  • Understanding of rotational dynamics and kinetic energy
  • Familiarity with the moment of inertia calculation for slender rods
  • Knowledge of angular velocity and its conversion to rpm
  • Proficiency in algebraic manipulation of physics equations
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  • Review the derivation of the moment of inertia for different shapes
  • Study the relationship between angular speed and kinetic energy
  • Explore the implications of mass reduction on rotational systems
  • Investigate practical applications of rotational kinetic energy in aviation engineering
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Students studying physics, aerospace engineers, and anyone interested in the dynamics of rotating systems and their energy calculations.

azila
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Homework Statement


An airplane propeller is 1.85 m in length (from tip to tip) with mass 97.0 kg and is rotating at 2300 rpm (rev/min) about an axis through its center. YOu can model the propeller as a slender rod.

What is its rotational kinetic energy?

Suppose that due to weight constraints, you had to reduce the propeller's mass to 75.0% of its original mass, but you still needed to keep the same size and kinetic energy. What would its angular speed have to be, in rpm?


Homework Equations


I = 1/12ML^2
after substituting, K = 1/2Iomega^2




The Attempt at a Solution



Ok, for the first part, I solved for inertia and I got inertia as 165.99. THen I plugged that into the kinetic equation and with the velocity is rad/sec which was 240.86, and got the kinetic energy to be 4.81 x 10^6, which is not the answer.

For the second part, I first found the mass without 75% of it to be 24.25 kg. So, I solved for Inertia again and got 6.92. Used that value in the kinetic equation to solve for omega and then converted that to rpm to get 112592 rpm which looks really weird and is not the answer.

Any help?? Thanks in advance...
 
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azila said:
Ok, for the first part, I solved for inertia and I got inertia as 165.99.
Redo this calculation.
 
thanks, I got it..
 

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