Is I=Mk^2 the Same as I=mr^2 in Physics Nomenclature?

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The discussion clarifies the equivalence of the formulas I = Mk² and I = mr² in physics, both representing the moment of inertia about the mass center. Here, M and m denote mass, k represents the radius of gyration, and r is typically reserved for a directly observable radius. The confusion arises from the different uses of the variable r in various texts, but both equations are fundamentally the same when defined correctly.

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SadPanda6022
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Hey guys, quick question.

I got confused in some nomenclature between some books and wanted to clarify somehow. A book I have has I=Mk^2 as defining a radius of gyration. Is this the same as I-mr^2?

Terminology was just confusing me.Thanks guys.
 
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Oops, I meant I=mr^2.

apologies
 
SadPanda6022 said:
A book I have has I=Mk^2 as defining a radius of gyration. Is this the same as I=mr^2?
It depends what r is supposed to be. Certainly
"I=Mk2, where M is mass, k is the radius of gyration and I is the moment of inertia about the mass centre"
is exactly the same as
"I=mr2, where m is mass, r is the radius of gyration and I is the moment of inertia about the mass centre".
But most writers reserve r to be a directly observable radius, such as the radius of a hoop or of a point mass in a circular orbit.
 

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