Initial Gyroscopic Precession Using Forces

[gyroscopeq]

I think I more or less understand how a gyroscope precesses--at least mathematically and in terms of torque/angular momentum.

My question here is: how does the gyroscope start precessing in the first place? The external forces on the center of mass are entirely vertical. Given that Newton's Second Law should always work, I don't see how there would not need to be an *external* force in the *horizontal* direction to get the COM initially moving in that direction. Obviously this means I am mis-understanding something. Does anyone have a good explanation of how this works and why I am wrong?

Thank you!

 

[A.T.]

The external forces on the center of mass are entirely vertical.

You mean gravity? Is that the only external force?

 

[gyroscopeq]

You mean gravity? Is that the only external force?

Gravity and a normal force.

 

[A.T.]

Gravity and a normal force.

What type of gyro are you talking about? A spinning top? Why do you assume that the contact force is vertical, it the CoM moves? Or, why do you assume that the CoM wouls still move, if the contact force was vertical (friction-less surface)?

 

[gyroscopeq]

What type of gyro are you talking about? A spinning top? Why do you assume that the contact force is vertical, it the CoM moves? Or, why do you assume that the CoM wouls still move, if the contact force was vertical (friction-less surface)?

I am imagining the simplest case: a spinning top on a frictionless surface. Would that no longer be able to precess?

 

[A.T.]

I am imagining the simplest case: a spinning top on a frictionless surface. Would that no longer be able to precess?

Does precession imply horizontal movement of the CoM?

 

[gyroscopeq]

Does precession imply horizontal movement of the CoM?

Yes? The CoM moves around in a circle.

 

[nearlynothing]

As you say, Newton's laws hold at all times and for each particle in the system.
What a force does on a particle is to change its linear momentum according to Newton's second law.
Now each particle on the spinning gyroscope already has a non-zero velocity in the first place, when
gravity acts, it acts downwards, but the resultant velocity won't be directed downwards because you
have to add the change in velocity due to gravity to the already existing velocity in each of the particles composing the gyroscope.
The net result of these changes is to change the plane containing the gyrocope as time passes, i.e. making it precess.

The force of gravity accelerates every single particle in the system, and the net effect of that is to make the gyroscope precess,
if no force acted on the gyroscope, that net result would never appear, so what makes the gyroscope start to precess is in fact gravity.

Edit: I should have said that what starts precession are both gravity and the normal force, since
these are all the external forces, but the whole argument still applies.

 

[A.T.]

I am imagining the simplest case: a spinning top on a frictionless surface.

The CoM moves around in a circle.

Think again. If the surface is frictionless, does the CoM really have to move horizontally, in order for the gyro to precess?

 

[gyroscopeq]

Think again. If the surface is frictionless, does the CoM really have to move horizontally, in order for the gyro to precess?

It does not. For some reason I had thought the "fixed" point was the point of contact of the top on the surface, not the CoM. Now I think it makes sense. Thank you!

 

[A.T.]

For some reason I had thought the "fixed" point was the point of contact of the top on the surface, not the CoM

The reason you thought this, is that its what usually happens, because the surface is usually not frictionless, so it can provide horizontal forces to accelerate the CoM. On a frictionless surface the CoM would be horizontally fixed.