Does Moment of Inertia Determine Mass?

AI Thread Summary
Two objects can have the same moment of inertia but different masses, as demonstrated by comparing a disc and a hoop with the same radius. The formulas for moment of inertia reveal that a disc and a hoop of the same radius can yield identical inertias while having different masses. This distinction highlights that moment of inertia alone does not determine mass. However, if two objects are identical in shape and density, their moment of inertia will correlate with their mass. Understanding this relationship clarifies the concept of moment of inertia in physics.
preluderacer
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Homework Statement


If two objects have the same moment of inertia, they must have the same mass.


The Attempt at a Solution



I think it's false but I can't figure out why.
 
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Take a disc and a hoop.

Idisc=MR^2/2
Ihoop=MR^2

I give a disc a radius of 1m, mass of 2kg. I give the hoop a mass of 1kg, radius 1m. The inertias are the same, the masses are not. Just one example of many.

If, on the other hand, two of the same type (density and shape) objects have the same moment of inertia then they ought to have the same mass.
 
thanks alot! i get it now
 
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