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Let's talk about a certain body.
This body is rolling on body 1.
It has a contact at point O.
Again, this is a rolling body.
If we know omega, the angular [velocity of] rotation of this body,
we can determine the velocity of that point C, the center, or the point B, or the point A in this body.
We know the magnitude (of the velocity), and for example, the velocity of point C is equal to omega multiplied by OC.
And similarly, the same formula will apply to the velocities of A and B.
With regards to the direction, we know that the direction of (velocity of ) point C will have to be perpendicular to the line OC.
Similarly, the velocity of point A must have a direction perpendicular to that line AO.
And the velocity of B also will have a direction perpendicular to line OB.
With regards to that fact that this is the instantaneous axis of velocity (of the rolling body),
we can easily make the analysis of the velocities of A, B and D [There is no D in the figure],
knowing the they relate to the distance AO and BO.
And by our graphical approach, we can just easily make this line,
draw this arc, and also draw this arc on B,
and knowing the velocity of C, we can make the proportionality line, and,
and know that the velocity of B which is here, will have a magnitude of this vector, and [the velocity of ] A has a magnitude of this vector.
Velocity of A, velocity of B.
And so again, this is the instantaneous axis of velocity, and it is a rolling body on this point, which is in contact with the body on which this body is moving.
If we can have this shape, or whatever shape it is, and it is in contact with this body,
and it is moving with a certain omega,
That point, for example, again, is a certain point which has to have a direction of velocity perpendicular to the line that joins that point D and point O, the contact point.
The velocity of that point also will have a certain direction perpendicular to that line.
Again, this has a direction, or the velocity of this point, let's call it point E and this is point F.
The velocity of all of these points will all have their directions perpendicular to that line that joins the points with the axis of rotation.
So, the instantaneous axis of velocity of these bodies are all these points of contact.
And if we may continue with this, if we know this as the direction of [velocity of] D, and if we can make this line,
and draw these arcs from E and F,
we can have this proportionality line,
and know that [magnitudes of the] velocity of F and velocity of E, knowing the [magnitude] of the velocity of D.