So I learned in physics what the first (mass) and second (inertial) moments are, but I am lost in what the actual concept of a moment is, devoid of the qualifiers. What is a moment?

Moment, sans qualifier, is usually a synonym for torque. For example, a pure moment results when the net force is zero but the net torque is non-zero. (Yet another term for this: couple.)

Why, then, are the first and second moments considered moments? Moment of inertia, as many understand it, can just be called inertia and refers to an intrinsic property of a specific geometric distribution of mass about a specific axis.

Part of the problem lies in misuse of the nomenclature. First and second moments should be called first moment of area and second moment of area. They really are all about area and not mass; lots of folks, me included, mentally extrude the area uniformly and turn it into pseudomass. That works, but it confuses the daylights out of new learners.

 

Both the first moment of area and the second moment of area have nothing to do with inertia. The first moment of area is commonly used to find the centroid of an irregular body. The second moment of area tells us how well a particular distribution resists bending and is commonly used in beam design.

 

Moment of inertia is about mass distribution. It looks a lot like the second moment of area (and, remember, I said lazy folks like me often use them the same), but it is different. Moment of inertia is a measure of resistance to angular acceleration.