What is the moment of inertia of the flywheel?

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SUMMARY

The moment of inertia of a flywheel used in an energy storage system can be calculated using the equation for rotational kinetic energy, Krot = (1/2)Iω². In this discussion, the maximum energy storage of 4.4 MJ at a rotational speed of 21,300 revolutions per minute (2.23E3 rad/s) was analyzed. The incorrect calculation of moment of inertia yielded 1.77E-3 kgm² due to a misunderstanding of energy units, mistaking 4.4 MJ for 4400 J instead of the correct value of 4.4 x 10^6 J. The correct approach involves setting 4.4 x 10^6 J equal to the sum of translational and rotational kinetic energy to solve for I.

PREREQUISITES
  • Understanding of rotational dynamics and kinetic energy equations
  • Familiarity with unit conversions, particularly between joules and megajoules
  • Knowledge of angular velocity and its conversion from revolutions per minute to radians per second
  • Basic algebra skills for solving equations
NEXT STEPS
  • Study the derivation and application of the rotational kinetic energy formula Krot = (1/2)Iω²
  • Learn about energy unit conversions, specifically between joules and megajoules
  • Explore the relationship between translational and rotational kinetic energy in mechanical systems
  • Practice problems involving moment of inertia calculations for various shapes
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Students in physics or engineering courses, particularly those focusing on dynamics and energy systems, as well as educators looking for practical examples of rotational motion concepts.

bikeeich
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Homework Statement



An energy storage system based on a flywheel (a rotating disk) can store a maximum of 4.4 MJ when the flywheel is rotating at 21,300 revolutions per minute. What is the moment of inertia of the flywheel?

Homework Equations



K= Ktranslational + Krotational
Krot= (1/2)Iω^2

The Attempt at a Solution



I solved 21,300 rev/min to be equal to 2.23E3 rad/s
I then tried to use this as angular acceleration in the Krot equation to solve for moment of inertia and got 1.77E-3 kgm^2, which was incorrect. I'm wondering if I need to set 4400J= Ktrans + Krot, to solve for I (moment of inertia) but if so I can't figure out how to solve for velocity in the Ktrans equation.
 
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bikeeich said:
I solved 21,300 rev/min to be equal to 2.23E3 rad/s
OK.

I then tried to use this as angular acceleration in the Krot equation to solve for moment of inertia and got 1.77E-3 kgm^2, which was incorrect.
Looks like you're off by a few powers of 10. Do that calculation over.

I'm wondering if I need to set 4400J= Ktrans + Krot, to solve for I (moment of inertia) but if so I can't figure out how to solve for velocity in the Ktrans equation.
No, you're on the right track.
 
I tried again and got the same answer. I'm sure I have a stupid mistake somewhere
Is it incorrect that 4.4MJ = 4400 J?
 
bikeeich said:
I tried again and got the same answer. I'm sure I have a stupid mistake somewhere
Is it incorrect that 4.4MJ = 4400 J?

4.4MJ = 4.4x10^6 J. 4400J is 4.4x10^3 J, or 4.4 kJ. :)
 
WOW. I might need to take a break. Thank you for the correction help!
 

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