Inertia with the parallel axis theorem

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SUMMARY

The discussion centers on calculating the moment of inertia of a uniform solid sphere using the parallel axis theorem. The moment of inertia about an axis tangent to the sphere's surface is derived as Ip = 7/5MR². The correct moment of inertia about the center of the sphere is Icm = 2/5MR². By applying the parallel axis theorem, the relationship between the two moments of inertia is established, leading to the conclusion that Icm = I - Md², where d equals the radius of the sphere.

PREREQUISITES
  • Understanding of the parallel axis theorem
  • Knowledge of moment of inertia calculations
  • Familiarity with solid sphere properties
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the parallel axis theorem in detail
  • Learn about different shapes' moments of inertia, such as cylinders and disks
  • Explore applications of moment of inertia in rotational dynamics
  • Investigate the implications of the moment of inertia in engineering design
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Students studying physics, particularly those focusing on mechanics, as well as educators teaching concepts related to rotational motion and inertia calculations.

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Homework Statement


A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center?


Homework Equations



Ip = Icm + Md2

Isolid sphere = 2/5MR^2

The Attempt at a Solution



This is what I tried:

Ip = 2/5MR^2 + MR^2
=7/5MR^2

I'm not sure what I'm supposed to do with this. I know that the correct answer is 2/7 but I don't know how you get that answer.
 
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In this case you're told that Ip = "I", where "I" is just meant to be some given value. You've already worked out from the parallel axis theorem that if the moment of inertia around the parallel axis is I, then the moment of inertia around the centre is I - Md^2, where d = r here.

You ended up with I = 7/5MR^2. If 7/5MR^2 = I, then what is Icm = 2/5MR^2 equal to in terms of the given value, I?
 

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