I'd like to follow up on a question I asked two years ago under the same title (Sept. 22, 2019).
I am trying to understand just exactly how angular momentum around the vertical axis is conserved during precession of a gyroscope. The moment we release the gyroscope, it begins to rotate around the vertical (z) axis that has its origin at the pivot point. Shouldn't something else have to start rotating in the opposite direction? If so, what is that exactly?
Last time, we got as far as saying that, in this open system, gravity exerts a torque on the gyroscope, causing it to fall slightly and give up a little potential energy to the kinetic energy of the precession. The torque induces a rotation around z. This leaves unanswered the question of conservation however.
An earlier answer indicated, in response to a follow-up question, that the earth itself would be induced to rotate (imperceptibly of course) in the opposite direction, so that angular momentum would be conserved, assuming the earth and the apparatus comprise a closed system.
How does the gyroscope induce the earth to do this? Of course the gyroscope exerts its own weak gravitational pull on the earth but wouldn't that simply drag the earth along with it - in the same direction? But we need a rotation in the opposite direction. How does that happen?
Also, the gravitation forces are acting vertically from gyroscope to earth and back, but the induced motion would need to be at right angles to them.
Sorry to ask the question again, but upon contemplation, the earlier answer didn't seem complete to me.