Moment of inertia of a cylinder

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SUMMARY

The moment of inertia of a cylinder can be calculated about its center of mass using the formula ∑miri². The discussion highlights the calculation of Izz as straightforward, while Iyy and Ixx present challenges that may require the application of double integrals. The parallel axis theorem is also mentioned as a useful relationship for simplifying calculations, particularly when transitioning from a disk's moment of inertia around an axis through its center in its own plane.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Familiarity with calculus, specifically double integrals
  • Knowledge of the parallel axis theorem
  • Basic principles of rigid body dynamics
NEXT STEPS
  • Study the derivation of the moment of inertia for a solid cylinder
  • Learn how to apply double integrals in calculating moments of inertia
  • Explore the parallel axis theorem in detail with examples
  • Investigate the moment of inertia for other geometric shapes, such as disks and spheres
USEFUL FOR

Students in physics or engineering courses, particularly those focusing on mechanics, as well as educators teaching concepts related to rotational dynamics and moment of inertia calculations.

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Homework Statement


Need to find the moment of inertia of a cylinder, about its center of mass, about the three principle axes. Z axis is normal to the circular faces of the cylinder. mass = M, radius = R, height = h

Homework Equations


∑miri2

The Attempt at a Solution


The Izz for whatever reason is trivial for me, easy to solve.
The Iyy = Ixx I'm having trouble with. I think it might be because this requires a double integral?
 
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What relationships have you got available to tackle this ? Familiar with the parallel axis theorem ? If you have ##I## for a disk around an axis through the center in its own plane, then your double becomes a single ...
 

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