Gyroscopic precession force diagram

[Elias Waranoi]

Hi, I've been learning about gyroscopic precession recently and I feel like I get it. I understand that when the flywheel of a gyroscope is spinning its angular moment plus the angular moment created by the torque from the force of gravity makes it turn. But I were thinking about the forces in a gyroscope and couldn't figure out what force is keeping the flywheel up. I know of the force of gravity and the normal force on the pivot connected to the rod connecting to the flywheel but to me that doesn't seem to be enough to keep the flywheel in the air. What's the other forces?

And bonus question, my physics book showed me that dθ = dL / L. I can understand this in a trigonometric way with tanθ = opposite / adjacent = dL / L. I can't make the connection between my knowledge in trigonometry and dθ = dL / L. The tanθ != dθ is what's bothering me.

 

[haruspex]

Hi, I've been learning about gyroscopic precession recently and I feel like I get it. I understand that when the flywheel of a gyroscope is spinning its angular moment plus the angular moment created by the torque from the force of gravity makes it turn. But I were thinking about the forces in a gyroscope and couldn't figure out what force is keeping the flywheel up. I know of the force of gravity and the normal force on the pivot connected to the rod connecting to the flywheel but to me that doesn't seem to be enough to keep the flywheel in the air. What's the other forces?

And bonus question, my physics book showed me that dθ = dL / L. I can understand this in a trigonometric way with tanθ = opposite / adjacent = dL / L. I can't make the connection between my knowledge in trigonometry and dθ = dL / L. The tanθ != dθ is what's bothering me.

It's not that there is a force keeping it up; it's that the torque from gravity, which is what you'd expect to make it fall over, has the paradoxical effect of making it precess instead.

By the way, you wrote of the gyroscope's angular moment (which is mormally termed angular momentum) and the angular moment (which should be just "moment") of gravity. I.e. you made them sound like they are dimensionally the same, but they are different. Angular momentum is ML²T^-1, whereas torque is ML²T^-2.

 

[A.T.]

I know of the force of gravity and the normal force on the pivot connected to the rod connecting to the flywheel but to me that doesn't seem to be enough to keep the flywheel in the air.

Normal force cancels gravity, so there is a force equilibrium. No other forces are needed. The video below might help you.

 

[Elias Waranoi]

Normal force cancels gravity, so there is a force equilibrium. No other forces are needed.

So if there is force equilibrium does that mean that the normal force from the pivot is the same size as the force from gravity?

 

[A.T.]

So if there is force equilibrium does that mean that the normal force from the pivot is the same size as the force from gravity?

The vertical forces must be equal but opposite if there is no vertical acceleration of the center of mass. Since the center of mass moves slowly in circles, the pivot must also provide a small horizontal centripetal force.

 

[haruspex]

Normal force cancels gravity, so there is a force equilibrium. No other forces are needed

True, but I interpreted the question as asking what counters the torque, which would make a pencil, e.g., fall over.
@Elias Waranoi , which were you asking? Maybe it was both.

 

[Elias Waranoi]

I was asking about force equilibrium. But I appreciate all the responses I get!

 

[A.T.]

I was asking about force equilibrium. But I appreciate all the responses I get!

The video I posted explains the issue in terms of linear forces and accelerations, which are more intuitive to most people, than torque and angular momentum.