Experiment at home

[m441]

Ok, thanks again. I will try to find this expression too.

Now, without friction, imagine a small weight on the point A when the point A is at bottom, with $\alpha=10$ degrees for example, the weight will move up (there is gravity) and win a potential energy and the wheel rotates a little and win a kinetic energy too. But the support don't receive any moment ?

[Theoristos]

It will due to inertia forces. Exact value depends on angular acceleration (and centrifugial force due to w0 too)
But it is the case of unbalanced disk.

[m441]

I suppose no friction. I start the device: I'm waiting $w0$ constant. The disk didn't receive any energy for the rotation around itself because it don't turn around itself. The only energy I gave to the device is the rotation of the red arm.

After, I apply the force F1 to the disk at a point that move up (a small force compared to the inertia of the disk), the disk apply the force F2 to the red axis and the disk receives F3. The disk receives a torque from F1/F3 this torque will increase the kinetic energy of the disk around itself, correct ? The support receives the force F2 but this force don't works, correct ? If the force F1 comes from a spring, the spring has more potential energy. How the energy can be constant ?

[Theoristos]

m441 в сообщении #1049625 писал(а):

I suppose no friction. I start the device: I'm waiting $w0$ constant. The disk didn't receive any energy for the rotation around itself because it don't turn around itself. The only energy I gave to the device is the rotation of the red arm.

In fact, not exactly. The disk have some rotation around the axis perpendicular to it axis of symmetry (w0 _sin(a)_ part). And corresponding kinetic energy too. Also, it have some _motion_ as solid body (as motion around the central axis), and corresponding energy.

m441 в сообщении #1049625 писал(а):

After, I apply the force F1 to the disk at a point that move up (a small force compared to the inertia of the disk), the disk apply the force F2 to the red axis and the disk receives F3. The disk receives a torque from F1/F3 this torque will increase the kinetic energy of the disk around itself, correct ? The support receives the force F2 but this force don't works, correct ?

Yes, only F1 will do a work. Due to rotation of disk.

m441 в сообщении писал(а):

If the force F1 comes from a spring, the spring has more potential energy. How the energy can be constant ?

I do not understand this part. What do you mean by "the spring has more potential energy" and "How the energy can be constant "?

[m441]

Theoristos в сообщении #1049781 писал(а):

In fact, not exactly. The disk have some rotation around the axis perpendicular to it axis of symmetry (w0 _sin(a)_ part). And corresponding kinetic energy too. Also, it have some _motion_ as solid body (as motion around the central axis), and corresponding energy.

I'm agree with that.

Theoristos в сообщении #1049781 писал(а):

I do not understand this part. What do you mean by "the spring has more potential energy" and "How the energy can be constant "?

I imagine a theoretical spring that can follow the wheel without friction (it's possible to imagine another thing than a spring). For apply the force I drawn, the spring must attract like that:



If the point I choose move up, the spring will extend itself and win a potential energy ?

The sum of energy must be keep constant (kinetic+potential+etc.) here the spring won a potential energy. The wheel increases its kinetic energy too because its angular velocity increases. And the support don't receive a torque so it don't lost an energy. If the spring win an energy and the disk too where an energy is lost ?

[Oleg Zubelevich]

m441 в сообщении #1049297 писал(а):

A support (grey color) turns at $\omega_ 0$. The axis of the purple disk is fixed on the support. The purple disk can turn around itself but at start the angular velocity is 0 (laboratory reference). Like that

you have a non-autonomous Lagrangian system with one degree of freedom and the constraint $\omega_0=\omega(t)$. Use the Lagrange equations

-- Вт сен 01, 2015 21:11:53 --

m441 в сообщении #1049797 писал(а):

I imagine a theoretical spring that can follow the wheel without friction (it's possible to imagine another thing than a spring). For apply the force I drawn, the spring must attract like that:

the same: all ofyour problems are from Lagrangian mech.

[m441]

Oleg: I'm teacher in software programming I don't know how to use the Lagrangian. I tested this experiment at home a lot of times and I find strange that the point A move up/down. So I would like to know if my experiment is false or not and sure if I can resolve with maths it's great. It's not that I don't want to work, I can resolve equations, integrals, but I don't know how to start the problem. If I have the start of the problem I can work on it.

[Theoristos]

Heh, looks like I got a problem. In fact, it quite fine and funny point.

m441 в сообщении #1049625 писал(а):

The disk didn't receive any energy for the rotation around itself because it don't turn around itself. The only energy I gave to the device is the rotation of the red arm.

The prolem is here.
Even there are no any friction, if $\alpha$ not equal 0 or 90 dergees, the disk will rotate around it axle.
The rotation speed will be different in ground system and system connected to gray disk, but it will rotate. Something a little similar to precession rotation.

[m441]

The angular velocity of the disk around itself is the same than the support at each time, even the support accelerates, or it is lower ? Because in my tests I'm agree that I accelerate because the friction is big (bigger than I would like to have) and I can see the angular velocity of the disk follows the support but there is a delay. Maybe you have the expression of the angular velocity of the disk around itself ?

[Oleg Zubelevich]

Let $\phi$ be the rotation angle of the purple disk around its inclined axis. This angle is counted relative to the support. Then the equation of the motion is as follows $\omega_0(t)\cos\alpha+\dot\phi=const$. The constant is calculated from the initial conditions

[Theoristos]

It's lower (also, it highly depends of the reference frame and exact $\vec{w}$component we are looking at).
It same in dull case when a=0.

Maybe the simpliest way for you will be to find some mechanical systems CAE and build test model there.

[m441]

Ok, and for the energy ? If the point A moves up it's possible to take something like the spring and apply the force F1 to the disk. The spring will increase its potential energy, the disk will rotate more and the support don't receive a negative torque ?

I simulate it with a 3d Ansys simulator to look the trajectory maybe tomorrow I will have the simulation ok.

[m441]

I simulated the device with Ansys, right the disk turns around itself even the friction is very low. The angular velocity is slower than the support (so a point can move up).

At start:



After:



I will do a video and post it later.

I have two questions:

1/ Why the disk turns around itself ? is it centrifugal forces or something else like the precession of a gyroscope (at start the disk don't turn around itself !) ?

2/ Where come from the energy, from the support ? In this case, how the disk can apply a torque on the support ?

[m441]

The video of the simulation (10s), the friction is very small, the angular rotation of the disk around itself at start is 0:

https://youtu.be/Pjc4dIf1aWI

The angular velocity:

[Theoristos]

m441 в сообщении #1050139 писал(а):

1/ Why the disk turns around itself ? is it centrifugal forces or something else like the precession of a gyroscope (at start the disk don't turn around itself !) ?

Not cetrifugal, in fact, but it depends on explanation.
The sipmliest way is to use non-inertial frame connected to support. When you give supplort angular acceleration, it appears to be "tangential" inertia forces applied to masses in this frame. The bigger radius - the bigger force. Some parts of inclined disk closer to support axis, some are farther. So, they have different forces and the disk begin to rotate.

m441 в сообщении #1050139 писал(а):

2/ Where come from the energy, from the support ? In this case, how the disk can apply a torque on the support ?

It's a funny qustion. The disk rotates not only around it axle. Can you split the total disk kinetic energy to parts? Maybe the disk with jammed axle wil have more energy than the free-rotating disk?