Moment of Inertia of Disk at any point

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SUMMARY

The moment of inertia of a disc about its center of mass is defined as 0.5mr². To calculate the moment of inertia at any other point, the parallel axis theorem is applied, which states that the moment of inertia about a parallel axis is equal to the moment of inertia about the center of mass plus mr², where r is the distance from the center of mass to the new axis. This theorem is crucial for understanding the moment of inertia for various shapes, including 3D objects.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Familiarity with the parallel axis theorem
  • Basic knowledge of rotational dynamics
  • Ability to apply mathematical formulas in physics
NEXT STEPS
  • Study the derivation of the parallel axis theorem in detail
  • Explore moment of inertia calculations for 3D shapes
  • Learn about the application of moment of inertia in engineering contexts
  • Investigate the relationship between moment of inertia and angular momentum
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Physics students, mechanical engineers, and anyone interested in the dynamics of rotating bodies will benefit from this discussion.

TheDestroyer
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As we know the moment of Inertia of a disc in the center of mass equals 0.5mr^2

My Simple question is: what is the moment of inertia of the disc at any other point? as I know there is a formula that supports the distance from the center of mass,

and is there a relation for 3D shapes?

Thanks
 
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Do you know the parallel axis theorem?

The moment of inertia for an object rotating about an axis that does not pass through its centre of mass, but which is parallel to it, is

mr^2 + (moment of inertia about an axis through the centre of mass and parallel to the other axis)

The r is the distance from the axis to the centre of mass.
 
Thank you, I know that law but this was 3 years ago, Thank you for reminding me, This post is closed!
 

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