Question

What does the principal-axis theorem suggest about the moment of inertia of an object with a spin axis that’s parallel but offset from one that’s through the center of mass vs. the moment of inertia of an object with a spin axis that’s through the center of mass? Can such a moment of inertia ever be smaller?

Answer 1

Principle axis theorem suggest that

I=Ig+mx^2

Where Ig =moment of inertia about center of mass.

m=object's mass.

x=distance of parallel axis and center of mass.

This theorem considers putting whole mass of system at its center of mass and considering it to be point mass. therefore, moment of inertia about parallel axis to center of mass can never be smaller than moment of inertia about center of mass, as above definition shows that