What is the orientation of the vector of friction?

  • #226
JrK
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the original friction question has been settled
If I have the right to add that case where I think your method doesn't work, if not the moderator can delete that message ? I imagine a circle that I blowed up (inflate), like a balloon but it is a circle. The radius of the circle increases more and more but the center of the circle is fixed to the ground. I drew the device at start and at end:

dd2.png

An enlargement to watch there is no friction:

df3.png



I used your method (look at the dot of contact, they are at the same place):

ddd.png


Enlargement:

dott.png


I replace the circle at the center just to see the magenta length:

dde.png


Enlargement:

deb.png


When I place the walls at the exact position, I need to count the movement of the magenta length. But there is no green length, the last drawing shows a difference of position of the dot of contact but look at the difference of length at the end of the walls, it is the same distance. I'm not sure at 100% there is no friction between the circle and the wall when I blow the circle, but the images seem to watch that.

The distance measure of friction is small but not exactly at 0, I measured: 0.03 but the distance calculated of the magenta length is 0.19, I can compare the lengths with the 2 following images at the same scale:

jzbv.png


gedd.png
 
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  • #227
A.T.
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... inflate ...
What does this have to do with your original scenario? It was rigid bodies only.
 
  • #228
JrK
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But the method is not universal ? it works for some examples not for others, so how to know if for an example it works or not.
 
  • #229
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But the method is not universal ?
The universal method is integrating force dot relative velocity.
 
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  • #230
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For me I don't have the right to do that:

hr-png.png
This is a trivial coordinate transformation to the rest frame of the wall.
 
  • #231
JrK
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I understood the problem (at least mine): the wall rotates around A0, but the wall doesn't rotate around the circle ! look the 2 positions:

gr3.png


If I place the circle at the same center:

gr23.png


And if the wall doesn't rotate around the circle, I need to correct its orientation just after rotate the group. So, the image :

fd6s3.png


is correct with your method.
 
  • #232
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I need to correct its orientation just after rotate the group.
If you do this, then it's not a mere coordinate transformation. You are changing their relative orientation and thus the physical situation.
 
  • #233
JrK
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Are you agree that the wall doesn't rotate around the circle ?
 
  • #234
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Are you agree that the wall doesn't rotate around the circle ?
Depends on what "rotate around a circle" means.
 
  • #235
JrK
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When you are fixed on the circle (you can see the wall), you see no modification of the orientation of the wall. You are fixed at the dot 'f' on the circle:

View attachment 262602

When the circle moves in translation and when in the same time the wall rotates around A0, you see the same orientation of the wall.
 
  • #236
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When you are fixed on the circle (you can see the wall), you see no modification of the orientation of the wall.
In your original scenario the wall changes orientation in the rest frame of the circle.
 
  • #237
JrK
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Yes, it is because I think with the dot of contact but I don't have the right...
Have you the equations of what I need to integrate to measure the length of friction ?
 
  • #238
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Yes, it is because I think with the dot of contact ...
It has nothing to do with their contact point. The wall rotates while the circle doesn't, so the orientation of the wall relative to the circle changes.
 
  • #239
JrK
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The universal method is integrating force dot relative velocity.
Have the equations I need to integrate ?
 
  • #240
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Have the equations I need to integrate ?
The 2nd equation in this section (v is the relative velocity of the materials in contact)
https://en.wikipedia.org/wiki/Work_(physics)#Mathematical_calculation

But in your specific scenario you can derive an analytical formula for the slip distance (sum of green and violet lines in post #179), and then multiply it by the constant force of friction.
 
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  • #241
JrK
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I have a question about the direction of the graphical method. I built all the drawings with the final position back to the initial, why ? (at the beginning of the thread I done that, without think of the direction) the true direction is from the initial position to the final. If I drew from the initial to the final I have less than d2, it is worst: I have less than d2. With basic examples, it is easy and from initial to final or the reverse it is the same result, here not at all.
 
  • #242
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With basic examples, it is easy and from initial to final or the reverse it is the same result, here not at all.
If you get different diagrams depending on what part you draw first, then that's more a problem with your consistency, rather than physics.
 

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