As a gyroscope precesses, its center off mass moves in a circle

[aaaa202]

my textbook says:

"As a gyroscope precesses, its center off mass moves in a circle with radius r in a horizontal plane. Its vertical component of acceleration is zero so the upward normal force exerted by the pivot must equal mg."

Now wouldn't this always be true. I mean if u have a flywheel attached to a pivot and at first don't let it spin. Then the weight of it produces a torque that makes the arm rotate till it hits something, e.g. itself or the table it stands on. But its not translating linearly, so isn't there also a normal force exerted upwards by the pivot in this case? It just doesn't produce a torque since it's distance to the rotation axis is zero.

 

[Doc Al]

Now wouldn't this always be true.

No. In your example of the non-spinning flywheel, the vertical component of acceleration would not be zero. It's falling. There would be an upward normal force at the pivot, but it wouldn't equal mg.

 

[aaaa202]

what would it equal then? And what is it that makes the pivot exert a normal force in the case, where the flywheel IS spinning?

 

[Doc Al]

what would it equal then?

Something less than mg. You could figure it out by computing the acceleration of the falling flywheel.

And what is it that makes the pivot exert a normal force in the case, where the flywheel IS spinning?

The flywheel has weight.

 

[aaaa202]

I don't get it. The flywheel isn't exactly falling it's just being rotated by the torque of its weight.

 

[Doc Al]

I don't get it. The flywheel isn't exactly falling it's just being rotated by the torque of its weight.

Its center of mass is accelerating downward.

 

[rcgldr]

If the gyroscope is not precessing at the exact rate required to keep it near horizontal, it's center of mass is accelerating vertically. It could be oscillating up and down at it's rate of precession also oscillates.

If the gyroscope's center of mass isn't accelerating downwards at 1 g, then there's some force applied at the post opposing gravity. If the center of mass isn't accelerating vertically, then the upwards force from the post is m g.