Inertia with the parallel axis theorem

AI Thread Summary
The discussion revolves around calculating the moment of inertia of a uniform solid sphere about an axis through its center, given its moment of inertia about a tangent axis. The parallel axis theorem is applied, leading to the equation Ip = Icm + Md², where Ip is the moment of inertia about the tangent axis. The user calculates Ip as 7/5MR² but is uncertain how to derive the correct answer of 2/7 from this. Clarification is sought on how to relate Icm to the given value I, ultimately emphasizing the need to manipulate the equations correctly to find the desired moment of inertia. Understanding the relationship between I, Icm, and the parallel axis theorem is crucial for solving the problem.
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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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