Where do the input energy go?

DaleSpam

If you want to test the situation in your drawing you will have to get two counter-rotating bicycle wheels mounted on the same axle. That is very different from just one bicycle wheel since one bicycle wheel can be given significant angular momentum, but two counter-rotating bycycle wheels won't have much.

Low-Q

I will use a more simple example.

I have a modified powerball that is fixed to a concrete floor.
Assume that I can turn the flywheel in it perpendicular to the flywheels rotation. Initially the flywheel does not spin. It starts to spin only when I turn it perpendiculary. If I stop turning it, its spin also stop. A gear mechanism makes sure of this.
So, the flywheel will under all circumstances spin in the vertical plane, and at the same time can turn in the horizontal plane - without exceptions.

I assume I will feel a counterforce as soon as I try to turn the flywheel perpendicular to its rotation, since the flywheel at the same time starts to spin perpendicular to the turn. Is that correct?

Say the flywheel is spinning constant at 10 000 rpm. And it turns around perpendiculary at a constant 60 rpm. If I successfully maintan this constant cycle over time, would that also mean that I have to apply energy to sustain the rpm in the vertical and horizontal plane except for making up for friction?

Vidar

DaleSpam

Based on the above discussion and your knowledge of physics, what would you guess and why? Think about torque and angular momentum. Think about torque and work. Which torques lead to what changes in angular momentum, and which do work, and why?

Low-Q

1. I would guess it takes energy to sustain the cycle, because the gyro don't want to turn in the same direction as the applied torque (As shown in the youtube video earlier where the two gyros are spinning in the same direction) - but the gyro in the powerball experiment has no other options other than turning in the same direction as the applied force.
Therfor I guess I must do work while turning the gyro around perpendicular to its rotation. (Suppose it is the same as fighting agains the angular momentum - applying energy to do so)

2. Which torques lead to what changes in angular momentum, and which do work, and why?
Not really sure where you're heading with these questions.

Vidar

DaleSpam

Since that leads to a failure of conservation of energy we know that this guess is wrong.

Why? Why do you think that work must be done in this case? What is the formula for work in angular motion? Does it apply here?

I am just trying to get you to actually analyze the device using sound physical reasoning.

Use this page as a reference
http://en.wikipedia.org/wiki/Torque
Especially the section on The relation to angular momentum and the section on The relation between torque power and Energy

Other sources are
http://en.wikiversity.org/wiki/Torqu...r_acceleration

And
http://bolvan.ph.utexas.edu/~vadim/C...11s/linang.pdf
http://www2.cose.isu.edu/~hackmart/torque.pdf

DaleSpam

Try to analyze it on your own first, but here are some hints.

Low-Q

Does "almost entirely along the axis" mean that the gear ratio isn't infinitely high? If the gear ratio was infinetily high, the angular momentum would be entirely along the axis?

I have now learned that precession will slowly turn the gyroscope in the same direction as the gyroscope is spinning. That precession will occour if a force, like gravity, is trying to overturn the gyroscope. Will it be possible to manually force the "precession" the opposite way if the gyro is still spinning the same way as before?
If so, what happens with the speed of the gyro?

Vidar

DaleSpam

Yes.

You can make the precession go either way simply by changing the direction of the external torque. Nothing happens to the speed of the gyro unless there are losses.

Low-Q

Thanks. I'm much wiser now :-)

DaleSpam

Excellent! You are welcome.

Low-Q

Sorry - not finished yet

I would think that the flywheel mass that constantly changes direction, and thus experiences a form of "pseudo" acceleration or G-forces, would require a certain amount of energy in order to do this.
Such as the "Coriolis" effect (Might be incorrectly expressed) of a centrifugal pump. Although the liquid can be returned to the pump input (a loop where the liquid repeats the same cycle), the acceleration of the fluid tangentially to the rotation as it flows away from the center of the pump will still try to prevent rotation. Where does the energy in such a system go? Will the liquid heat up?

Vidar

DaleSpam

No worries. Questions and answers are not rationed here

Neglecting losses precession does not require energy in general. This is because the torque is perpendicular to the axis of rotation. Just like a force perpendicular to motion does no work, for the same reason a torque perpendicular to the rotation also does no work. We have analyzed this specifically for your geared gyroscope, but it applies to precession in general.

Yes, in this case the system is not frictionless. For fluids, this kind of friction is called viscosity.

Low-Q

OK, thanks. I just visualized the experiment where I place a red dot on the flywheels circumference. I rotate the flywheel 1 rps, and the flywheel have a circumference of 1 meter. The red dot travels now at 1m/s. If I turn the flywheel perpendicular to its rotation 1 complete turn per second, the red dot will cover a longer distance per revolution of the flywheel, and increase velocity by how much? Do you have an equation for this?

Vidar

DaleSpam

I don't have that equation, although it shouldn't be too hard to derive.

Low-Q

I have drawn an illustration in Google ScetchUp - hope you understand it.

It is a fast spinning flywheel (red) on a shaft (Blue). Two green guides prevents the shaft and the flywheel to move sideways.

Gravity is pulling on the heavy flywheel.

Question:
As the spinning flywheel starts falling from the top (Not illustrated). Will the velovity of it be greatest at point A, B or C?

What velocity can we expect at point A, B and C?

Will the shaft with its spinning flywheel behave as longer pendulum (Kind of a pendulum in slow motion)?

Vidar

Attached Thumbnails

 

Low-Q

Ofcourse, velocity cannot be known with unknown RPM of the flywheel, its weight, and length of the shaft. Forget that question.

Anyone?

Vidar

DaleSpam

That is a really annoying system to analyze. The weight will cause a torque about a horizontal axis which will try to get the gyroscope to precess horizontally. It will then run into the green guide which will exert a force to prevent its horizontal precession. This force will also generate a torque, this time about the vertical axis. The torque about the vertical axis will cause the gyroscope to precess either up or down until it reaches the top or the bottom. At that point gravity will no longer be exerting a torque and it will just stay there. It will not act as a pendulum.