Is r in the Moment of Inertia Formula Always the Shortest Distance?

[jono90one]

for "r" in mr^2 is it the shortest distance?
(consider a square with point mass at the corners connected by rods, r is closer if you take the diagonal height rather than the rod distance.)

 

[chaoseverlasting]

Can you give us the context in which this was stated?

 

[Filip Larsen]

In general, the term mr² refers to the mass and distance from a reference axis of a single particle (i.e. a point-like mass distribution). If you have a square of point masses in the corners, you have to consider each point mass as contributing to the moment of inertia by that term. If your rods have mass that is, say, evenly distributed along their length, you have, in principle, to integrate moment of inertia r²dm along the length of the rod (with varying r) in order to get it for the whole rod. See for instance [1] for an introduction.

In practice you can look up the moment of inertia for many geometrical shapes and mass distributions in handbooks, transform those moments to a common reference axis and then add them. Or you let your CAD system do it for you.

[1] http://en.wikipedia.org/wiki/Quantum_entanglement