What is the orientation of the vector of friction?

[A.T.]

You spoke about what image ? the image of the message # 147 is the second case: no translating, rotating.

Your scenario is case 3: translating and rotating relative to the wall. The other cases were just a decomposition of case 3 into the two components.

Draw your scenario, in the rest frame of the wall, just as I explained:
- Draw both time-points in your original frame
- Rotate each time-point-image around the wall-pivot, such that the walls align (and ideally are horizontal)

 

[JrK]

I'm not sure to understand, is it the case 2 ? :

We are agree that the wall at 45° is fixed (not the 30°) ?

 

[jbriggs444]

I thought that case 2 was rotating, not translating. In #152 you show three circles. Are we to understand that GRAY is the before, GREEN is the after and BLUE is irrelevant? If so, that's neither rotating nor translating. That's glued-to-the-wall.

 

[JrK]

I thought that case 2 was rotating, not translating. In #152 you show three circles. Are we to understand that GRAY is the before, GREEN is the after and BLUE is irrelevant? If so, that's neither rotating nor translating.

You speak at me ? For me, blue is the start, green the end and gray is the modification asked by AT. In fact, I don't understand what I drew :p but I try. The wall fixed is at 45° not 30°. It is very strange that I drew. I need help. In fact, what I do with these drawing ?

 

[jbriggs444]

You speak at me ? For me, blue is the start, green the end and gray is the modification asked by AT. In fact, I don't understand what I drew :p but I try. The wall fixed is at 45° not 30°. It is very strange that I drew. I need help. In fact, what I do with these drawing ?

If you do not understand what you drew, how do you expect us to?

If you are trying to depict rotation without translation then depicting translation is not appropriate.

If you are trying to depict rotation with translation then the BLUE transitioning to GRAY is correct in everything except, possibly, scale and the GREEN is irrelevant.

It would help if you put enough commentary with your drawings that we know what you are trying to depict. Extraneous circles and extraneous walls are not helping.

 

[A.T.]

View attachment 261958

Good, now do the rest:

Then draw the path of the contact point on each body:
- a line on the wall (same length as circle_displacement )
- an arc on the circle (rotation_angle * circle_radius)
The total slip length the the sum of them.

Hints how to make your life simpler:
- Make the wall with the 2 circles horizontal
- Make the cross-marking initially go through the contact point.

 

[JrK]

@AT: we are agree that :

is the case 1 ?

So the path of what from what ? I think I don't take in account the end position (green). So here if it is well the case 1/, what path on the wall ?

 

[A.T.]

is the case 1 ?

No, the cases I listed refer to the motion in rest frame of the wall. So you first have to transform correctly into that frame. Which you finally did in post #152, so now proceed as described in post #156.

 

[JrK]

But you confirmed the #152 is the case 2/ (I asked, you reply: good) so I need the case 1/ no ?

 

[A.T.]

But you confirm the #152 is the case 2/

No, #152 is your scenario, which is case 3: Relative to the wall the circle is translating and rotating (compare blue and grey circle).

 

[JrK]

No, #152 is your scenario, which is case 3: Relative to the wall the circle is translating and rotating (compare blue and grey circle).

Ok, so the length I measure is d1, BUT like I said before you forget the movement of the dot of contact between the circle and the wall RELATIVELY to a fixed dot on the material (the circle for example) and the distance moved by the dot of contact is d1-d2. So, your slip of the friction is well d2.

 

[A.T.]

Ok, so the length I measure is d1,

There is no d1 in image #152. Please follow the instructions in post #156.

 

[JrK]

That ?:

 

[A.T.]

That ?:

View attachment 261969

No.

Hints how to make your life simpler:
- Make the wall with the 2 circles horizontal
- Make the cross-marking initially go through the contact point.

 

[JrK]

Make the cross-marking initially go through the contact point.

I don't understand.

I place the circles horizontal and after ? It is A0 on the dot of contact ? :

Or maybe it is :

I see the mark on the left circle and on the right circle. The length of the friction is that distance ?

 

[A.T.]

I don't understand.

I place the circles horizontal and after ? It is A0 on the dot of contact ? :

View attachment 261971

Good, now adjust the dotted-markings such that initially one of dotted lines hits the contact point. For the final state they are rotated counter-clockwise from the initial state.

Then mark in different colors:
- the part of the wall that was in contact with the circle
- the part of the circle that was in contact with the wall

 

[JrK]

now adjust the dotted-markings such that initially one of dotted lines hits the contact point. For the final state they are rotated counter-clockwise from the initial state.

You want I rotate the circles ? only one ? in which direction CW CCW ?

 

[A.T.]

You want I rotate the circles ? only one ? in which direction CW CCW ?

Both by the same amount, so the initial contact point is marked on the circle. And use only one radius line for that, not 4 of the same color making it ambiguous,

 

[JrK]

But the initial marks on the two circles are already in contact with the wall. Which amount to rotate ? CW or CCW ?

 

[A.T.]

But the initial marks on the two circles are already in contact with the wall.

I mean the oblique dotted lines through the center of the circle. The are useless.

For the initial state draw a single radius to the initial contact. Then for the final state the same marking rotated with the circle CCW.

 

[JrK]

I drew that:

It is correct ?

 

[A.T.]

I drew that:

View attachment 261973

It is correct ?

No. The new solid line mark cannot rotate relative to the old dotted line marks. They are all just marks on the same circle. They have to rotate with the circle in the same way.

Is this not obvious to you?

 

[JrK]

Is this not obvious to you?

I don't understand what I'm doing in the geometry, nor where I'm going. I do what you ask but I don't understand the method. And like your english is technical I have difficulties to draw what you want. It is a true method tested ?

 

[A.T.]

I don't understand what I'm doing

You have added a new mark on the blue circle, right in the middle between two old dotted marks.

For the grey circle that new mark must also be right in the middle between two old dotted marks.

 

[JrK]

like that ?

 

[A.T.]

like that ?

View attachment 261974

Yes. Now:

Then mark in different colors:
- the part of the wall that was in contact with the circle
- the part of the circle that was in contact with the wall

 

[JrK]

green: wall in contact with the circle
violet: circle in contact with the wall

?

 

[A.T.]

View attachment 261975green: wall in contact with the circle
violet: circle in contact with the wall

?

Why does green go beyond the final contact point?

 

[JrK]

so like that:

 

[A.T.]

so like that:

View attachment 261976

Yes.

The total slip distance is the sum of the green and violet length. This is the distance that you put into F * d to compute the energy dissipated by friction.