How to Calculate Moment of Inertia for a Solid Disk with Central Hole

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SUMMARY

The discussion focuses on calculating the moment of inertia for a solid aluminum disk with a central hole, specifically with external and internal diameters of 13 inches and 0.6 inches, respectively, and a thickness of 0.5 inches. To find the moment of inertia, users are advised to first calculate the mass using the density of aluminum (2.70 g/cm³) and the volume of the disk. The formula for the moment of inertia is confirmed to be I = M * r², where M is the mass and r is the radius. This foundational understanding is essential for solving similar pre-lab problems.

PREREQUISITES
  • Understanding of geometric volume calculations
  • Familiarity with the concept of moment of inertia
  • Knowledge of density and mass conversion from g/cm³ to kg/m²
  • Basic algebra for manipulating formulas
NEXT STEPS
  • Learn how to calculate the volume of a solid disk with a central hole
  • Study the derivation of the moment of inertia formula for composite shapes
  • Explore unit conversions between grams, centimeters, kilograms, and meters
  • Practice solving similar physics problems involving rotational dynamics
USEFUL FOR

Students in physics or engineering courses, educators teaching mechanics, and anyone needing to calculate the moment of inertia for composite objects.

bcalkins
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Consider a solid disk made of aluminum with a central hole as shown in the figure - can't include...don't believe it's necessary. The external and internal diameters are found to be 13 inches and 0.6 inches. The disk is 0.5 inch thick. The density of aluminum is 2.70 g/cm3. Question:
Calculate the moment of inertia of this disk for rotations about its axle, in kg m2.

I have no idea how to determine the mass of a disk. I believe to determine the moment of inertia I use the formula Mxr^2

Formulas would be VERY much appreciated. I have several more problems on this pre-lab that are similar to this question. Thank you very much!
 
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Think of 2.7g/cm3 as a formula to find mass if you have volume in cm3. Therefore maybe start with finding the volume of the disk.
 

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