# The position of a point in 2 rotations with 2 axes

## Homework Statement

It's a question I ask to myself. A support turns at ##w_0## and can accelerate. A disk on the support can turn around itself (side view) but at start ##w_1=0##. I done the experimentation with 2 wheels but I'm not sure about my tests. There is an angle between 2 axes:

## The Attempt at a Solution

If the angle ##\alpha=0## the point A (A if fixed on the purple disk) is not always at the same position in the support, like that (top view):

Now, if the angle is at 1° is it the same ?

And the angle at 20° is it the same ?

I tested a lot of time and I can see the point A is always like that. If it's true, it would say the point moves down and after up (etc.) when the support rotates (in the side view).

The velocity of the up/down of the point changes with the angle. When the angle is at 90° the point A never moves up or down. So it seems the law is with a cosinus of the angle.

The purple disk can't turn around itself if I accelerate the support so the point A must be like I drawn in the top view, even the angle is not 0, but I find strange that the point A move up/down.

Is it the same if I accelerate the support ?

If you could explain to me if there is an error please ?

## Homework Equations

Only a question to myself.

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The angle is more like that in fact:

I tested with an angle from 0° to 20° and with ##\omega_1=0##: the point A moves up/down like I drawn before, I can't test with an higher angle.

Does someone knows if the point A changes its "altitude" when the support rotates and ##\omega_1=0## ?

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Nobody knows ?

I tested all this afternoon and I see the point A moves up/down like I drawn.

Nobody ? The question is not clear ?

Hello,

I simulated it on Ansys Spaceclaim. It's ok, a fixed point on the disk moves up/down like I thought (altitude from the ground). The disk rotates around itself without friction and even at start there is no rotation around itself but the angular velocity is lower than the support. The support rotates at ##\omega_0##

The video of the simulation, I drawn a fixed black circle on the support to look at the rotation of the disk around itself:

The angular velocity (example, the angle from the vertical is at 62°):

The angular velocity of the disk (without friction) is ##cos(\alpha) \omega_0## with ##\omega_0## the angular velocity of the support, and ##\alpha## is the angle of the axis of the disk from the vertical.

I understood why the disk rotates at start around itself.

Like the disk rotates around its center of gravity and around itself it has more energy than it rotates around its center of gravity only. So the support must receives a torque at start. Maybe the torque is like that :

I'm not sure because I can reduce the thickness of the part of the disk in contact with the support. Have you an idea how the support receives a negative torque from the disk to have the sum of energy constant at each time ?

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