Quote from: Omnibus on May 22, 2009, 04:43:12 PM
@mondrasek,
 

I'm posting for the second time how I'm drawing weight vector and it is obvious that I'm not drawing vectors from the weight vector normal to the moment arm. You should acknowledge at once that you're wrong. Otherwise it's just an irrational exchange.

You are correct.  I did not state that well.  I retract that statement and openly admit I was wrong.

Quote from: Omnibus on May 22, 2009, 04:43:12 PM
The ball and the slot are one. I already explained why the way the ball is attached to the system to be rotated has no impact on the magnitude and sign of the torque. The only thing that has a bearing on the magnitude and the sign of the torque is the distance from the center of mass to the axle and the vector normal to that distance, derived from the weight. As I've said many times already, the product of this distance (arm) and the normal can never be greater than that product in absence of guides.

And here is where you are completely wrong.

For the case in dispute the weight is supported by two surfaces.  The correct vector math is to resolve the weight vector to the normal of those two surfaces. 

Please read that again.

The method that you hold as correct does NOT resolve the weight vector to the normal of the slot, only to that of the guide.  Instead, you resolve it to the normal to the motion path.  But there is no surface on the wheel that the weight is in contact with that is normal to the same angle as the motion path.

There are two surfaces the weights are in contact to in this case.

1)  The guides, which you are calculating correctly.

2)  The slots.  This angle you are mistakenly replacing with the normal to the angle of the motion path.  There is no surface at that angle.  The correct surface and angle is that of the slots.

M.

Here is the problem.

The two cyan components. One is pointing below the guide. one is pointing above the guide. How can that be? if they were both to one side of the guide, then there would be no interaction, but one or the other must be interacting.

@mondrasek,

I've said it many times already, I said it in the last post and I'm saying it now --  the sphere is part of the moving system and it doesn't matter how it is attached to the rest of it, the torque it creates will only depend on whether or not there are guides. It doesn't matter whether the sphere is glued to the arm, has an elaborate way of attachment to the arm with one, two, three or many surfaces -- the torque it will cause will be the same. Contact surfaces, part of the moving system have absolutely no bearing on the torque. Only outside influences (guides), outside of the moving system, which redirect the motion and change it from the circular (without the guides) influence the torque, at that, diminishing it.

The weights are NOT attached to the wheel on the left hand side.

The weights are leaning against the wheel on the left hand side.

The weights are in slots and are free to slide closer or further from the axle on the left hand side.

M.

Quote from: stgpcm on May 22, 2009, 06:00:34 PM
Here is the problem.

The two cyan components. One is pointing below the guide. one is pointing above the guide. How can that be? if they were both to one side of the guide, then there would be no interaction, but one or the other must be interacting.

Cyan vectors are the components of the tangential component of the weight vector and are applied where the center of mass is, lying on the Grey line. Obviously, the Grey line (where the center of mass at all positions of the wheel resides) runs parallel to the physical guide. This is simplified presentation of the wheel we're discussing, focused only on the forces that act at this given position of the wheel.