DaleSpam,
Thank you for taking the time to write those examples; they were enlightening, and I agree with your statements.
Originally, regarding couples, I didn't want to trust the math because my naïve gut feeling of how a system would behave was wrong. I accept now that my gut feeling is...
I don't think you're being dense; I should have said "couple" in the quoted text in post #8.
In post #7, I was just using "moment" to illustrate what I meant by "placed at a point".
Maybe an assumption of mine is wrong: Imagine drawn on paper an object (unit thickness into the paper). If we...
Maybe I should write: "What DOES happen to the steering wheel when we apply a moment about an axis passing through the steering wheel handle at the 3 o'clock position and perpendicular to the paper?"
"Placed at a point" is just an indication of the location about which something rotates. Imagine a two dimensional object with a force acting on it (in the same plane as the object). Find the moment of the force about "a point" O on the object. The result is a vector pointing out of (or into)...
I agree with your first paragraph.
For the case of the couple being placed at the 3 o'clock position on the steering wheel, I would expect the couple to affect rotation of the wheel about that point (about the wheel handle at the 3 o'clock position). However, the reaction force in the axis of...
I'm phrasing the example differently to try to avoid misunderstanding:
We have a steering wheel. A force, F, is applied downward on the wheel handle at the 9 o'clock position; and there is another force, F, applied upward on the wheel handle at the 3 o'clock position. And say that the wheel...
We read that the a couple is a free vector, i.e it does not depend on the point of application.
However, please consider the following example: If you apply two equal magnitude forces anti-parallel to each other, one on each side of the wheel, a couple is formed, and so the wheel will rotate...