Precession, Weight & Conservation of Angular Momentum

[GwtBc]

Many of you might have seen veritasium's video on the "Anti-gravity wheel". Through one of the comments, I was introduced to the idea that the reason the apparatus is so easy to lift is because the energy to do so comes from the spin of the wheel, i.e. its rotation slows down as it is lifted and speeds up again as it's lowered.

This accounts really well for the fact that the lifting of the gyroscope doesn't seem to affect the reading on the scale, aside from the fluctuations that you might expect given the circumstances. However, my problem with it is that it seems to violate conservation of angular momentum. The only torque exerted is that due to gravity, which is manifested in the precession itself. So where does this other retarding torque come from? Additionally, if I'm correct in saying that this contradicts conservation of angular momentum, how come a wheel traveling up a hill loses rotational energy? There also doesn't seem to be any retarding torque there. Maybe a little bit due to air resistance but that would be negligible compared to that provided by friction. Is the rotational energy also being converted into GPE, just like the translational energy? If so by what process? Surely energy can't be transferred in this scenario without the presence of a force...

 

[A.T.]

where does this other retarding torque come from?

What do you mean? Friction that slows down the rotation?

Surely energy can't be transferred in this scenario without the presence of a force...

The hand provides the vertical force to support the weight and provide vertical acceleration.

 

[GwtBc]

What do you mean? Friction that slows down the rotation?

What force slows down the rotation of a wheel as it moves up a slope? Or, in this case, as it ascends vertically up. (assuming that this idea where the energy for the climb is provided by the rotation of the gyroscope is true, and I'm really not sure that it is, that's the main question really)

The hand provides the vertical force to support the weight and provide vertical acceleration.

I was referring to the loss of rotational energy as a wheel moves up a cliff there; but since you mentioned it, if the hand is exerting an appreciable force, then why doesn't the reading on the scale change? Again this related back to my question. If the hand is forcing the weight up, then that doesn't explain why the scale reading doesn't change as the object is lifted, and if it's not and the energy is provided by the slowing of the rotation of the wheel (not the entire system) around it's axis, then where is the torque that causes the change in angular momentum.

 

[jbriggs444]

What force slows down the rotation of a wheel as it moves up a slope? Or, in this case, as it ascends vertically up. (assuming that this idea where the energy for the climb is provided by the rotation of the gyroscope is true, and I'm really not sure that it is, that's the main question really)

The idea that the energy for the climb is provided by the gyroscope is not true.

In the case of a wheel climbing a slope, the wheel is applying a rearward/downward force on the ground and ground is applying a forward/upward force on the surface of the tire. The force of the ground on the tire has two effects on the wheel, both of which have full effect simultaneously.

1. Viewed in the ordinary linear sense, the force from the ground is driving the wheel upslope.
2. Since the force from the ground is offset from the wheel's axis, it also amounts to a retarding torque, slowing the wheel's rotation.

The key thing is that for a wheel rolling up a slope, the torque is aligned with the wheel's rotation and can result in a change of the magnitude of the wheel's angular momentum. In the case of a gyroscope, the torque is at right angles with the wheel's rotation and can only result in a change of the direction of the wheel's angular momentum.

 

[A.T.]

If the hand is forcing the weight up, then that doesn't explain why the scale reading doesn't change as the object is lifted

It only changes when it is accelerated, not when it's lifted at constant speed.

then where is the torque that causes the change in angular momentum.

Depending on the reference point, it's either gravity, the hand or both.

 

[GwtBc]

It only changes when it is accelerated, not when it's lifted at constant speed.

But it must be accelerated initially, yet there's still no change.

 

[jbriggs444]

But it must be accelerated initially, yet there's still no change.

That is not correct. There is a change.

 

[GwtBc]

is it too small to be registered by a regular scale?

 

[A.T.]

is it too small to be registered by a regular scale?

He accelerates it gently during the lift, so it doesn't stand out that clearly from the noise, and oscillation such a scale has. You can see the effect better during lowering, where the scale drops below weight (start lowering) and then goes above weight (end lowering). If the lifting was done as quick as the lowering you would see the same effect on the scale there, just in reverse order: above weight (begin lifting) then below weight (end lifting).

But in both directions, the average scale reading for the whole height change (between two time points with zero vertical velocity) is equal to the weight you read statically. Also, in the phase where the total center of mass (man and gyro) moves vertically at constant speed (very difficult to realize in such a experiment) the scale reading is also equal to the weight you read statically.

And for all above, the scale reading is not affected by the rotation of the gyroscope.