Couple, Torque, Moment of Inertia

Couple:Two equal and parallel forces acting in opposite direections; opening a tap with 2 fingers, undoing a nut using a wheel brace with both hands.

Moment of a couple is the product of the force and the perpendicular distance between them.

Torque is the turning effect of a force. Like undoing a nut witha spaner. If you can't undo it you'll try with a longer spaner. Still if you fail, you may try a pipe to extend the lever arm to undo a nut.

Torque = Force X perpendicular distance.

Moment of inertia is the property of the body to continue to stay in motion.

Give the same angle of displacement to a short and a long pendulum (both having the same mass) and see which stays in motion longer. This is because the Radius of Gyration is greater for the longer pendulum.

Moment of Inertia = mass X (Radius of gyration)2

All of this is good stuff. I'd add that "moment" when used alone, is synonymous with "torque", so you could say that a wrench creates a moment of 10 Newton-Meters or a torque of 10 Newton-Meters.

There are two (or more) common ways in which "moment of inertia" is used. In one, you are interested in knowing the distribution of masses because you want to know at what rate something might oscillate, or react. (In racing cars, moment of inertia is kept small -- in other words, masses are concentrated near the center -- so that the car reacts very quickly to steering inputs.)

In the other sense, or other usage really (the calculation is identical) you are interested in distribution of masses not because of some oscillation, but because you are trying to calculate (for instance) the deflection of a beam made of a square or rectangular tube. As you can imagine, if all the material in the beam is located along the centerline of the beam, it will flex easily, and if it is located near the outside, it will be stiffer.

This is probably shaving the point finer than you need right now.

From the context it looks as if the moment of inertia he's asking about is that of a rotating body, kg.m².

The other MoI, used in beam calcs etc, m⁴, I think is preferably called "2^nd moment of area" to avoid confusion.

I agree, both that he is probably looking for kg.m2. and that "2nd moment of area" is better.

Oddly, my Bosch automotive handbook adds to the confusion. On page 48, headed "Moments of Inertia." there is this reference: "See page 59 for second moments of area." If you go to page 59, you find the title: "Section moduli and moments of inertia of plane areas." That page contains a reference back to page 48: "See p. 48 for moments of inertia of mass". One could conclude we make this stuff up as we go.

AND..........I might add, "Every couple has its moment".

LOL. Each day there is a post that brightens that day...