Moment of Inertia of a Quarter Disc

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SUMMARY

The Moment of Inertia of a quarter disc with mass M and radius R about the axis passing through the center and perpendicular to the plane is calculated using the formula for a full disc divided by 4. The initial confusion arose from incorrect mass usage, which led to an erroneous result. The correct approach confirms that dividing the Moment of Inertia of a full disc by 4 is indeed valid when the mass is accurately accounted for.

PREREQUISITES
  • Understanding of Moment of Inertia concepts
  • Familiarity with the properties of a disc in physics
  • Basic knowledge of calculus for integration
  • Ability to apply mass distribution principles
NEXT STEPS
  • Study the derivation of the Moment of Inertia for different shapes
  • Learn about mass distribution and its effect on Moment of Inertia
  • Explore integration techniques for calculating Moment of Inertia
  • Investigate applications of Moment of Inertia in rotational dynamics
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Physics students, mechanical engineers, and anyone studying rotational motion and dynamics will benefit from this discussion.

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1. Find the Moment of Inertia of a Quarter Disc which has mass M and radius R about the axis passing through the center (of original disc) and perpendicular to the plane.

2. The attempt at a solution
I found the Moment of Inertia (I) of a disc about the axis passing through the center, perpendicular to the plane and divided by 4. It gave the wrong answer.

So, please tell me that why dividing by 4 is giving me the wrong answer for the quarter disc.

Also, a hint of how should I start the problem.
 
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Dividing by 4 is correct. Did you use the correct mass? (I suspect that's the problem.)
 
Doc Al said:
Dividing by 4 is correct. Did you use the correct mass? (I suspect that's the problem.)

Yes, I got it correct now.


Thanks
 

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