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Now let's look at physics.
And from the physics point of view I am going to make a model.
And the model is going to be mechanical.
And the model is going to be based on the picture of ...
... of the plot of all the points.
So I will ...
Let me ...
... stick with ...
... only four points just to avoid making picture overcomplicated.
And what I will do is I will ...
How to find a line on this plane?
Fix these points the best way.
Now how do you do that?
Well the mechanical way would be to make a straight rod.
Metal rod that never bends.
And then try to bring it close to this point, and close to that point, and close to that point ...
Close to every single point.
Without bending. Right?
How you bring that rod close to this point?
Well mechanically you can put it spring.
So that it pulls the rod toward that point.
And for simplicity I'd like this spring to be vertical.
So we think about a spring here.
And a spring there.
And all the springs are stretched.
And all these springs are pulling the rod toward the corresponding point.
So then I let them go.
And then of course it is quite possible that those forces will turn the rod a little bit.
And that means that the point of contact of the spring will not be vertical any more.
So there is some mechanical adjustment we can make.
[...] ...
... a sleeve on the rod so that the rod goes freely through that sleeve.
And they pull actually that sleeve.
So that the spring ...
... remains vertical all the time.
And that spring remains vertical all the time.
And there is [...] I'm afraid of ...
... all those springs will not vertical.
[...] some angles.
[...] angles.
They don't want.
So ...
Even if the springs are all vertical and they make them vertical ...
... I still hope that all the springs pulling the rod ...
... will make the rod stabilized at some point.
So the rod will stop moving after some time and ...
And of course at this point you either think about this plane being horizontal ...
... so that the gravity doesn't pull rod ...
... pulls extra to the ... extra down.
Or you think of rod having no weight.
So the gravity is not effecting the picture.
The only important thing is how these springs are pulling the rod toward their points.
And of course these are fixed points. Think of [...].
One end of spring is fixed, the other is moving.
All right? So are you clear about the system?
Do we expect it to stop at some equilibrium so that the rod is ...
... hopefully the closest way to all the points?
All right. Well then how do you describe the equilibrium in physics?
Is it going to be equilibrium of that rod?
When is it that an object, a solid object is not moving in physics?
Well all the forces are acting. Right?
So there are forces ...
.. let's say f one ...
... and f two ...
... and f three ...
... and f n.
So n forces acting on the rod.
Student: [...].
When the net force is equal to zero.
When the sum of all the forces is equal to zero.
So the equilibrium condition ...
... is when this sum of all the forces ...
... is equal to zero.
Is that it?
All right. Let me [...]. You may prefer physics better.
But you have to be careful ...
... understanding that whether this is the condition.
Or there is something else to say.
What this condition guarantee that the rod will not move at all.
Student: [...]. NB: Moments?
[...] forget about the moments?
Student: [...].
Don't you want the moments to be zero?
[...].
You can have a rod. And you can have one force acting this way.
Another acting that way.
So the sum of the forces, the sum of these vectors is zero.
But you do not expect the rod to be ...
... in equilibrium, right? It will rotate.
So what makes it rotate is the momentum.
So what's the momentum?
Strange [...].
Student: [...].
So ...
So the [...] of momentum is that does it really matter ...
... which point you fix and look at momentum with respect to that point?
So I will fix this point.
And I will look at momentum of each force with respect to that point.
So ...
This is a sum of ...
... all the way to n ...
... momentum ...
... of F_i ...
... with respect to that point ... well, I don't know ... P.
Let's call it P.
To be zero. It is the second condition.
Is that a complete list? Well of course you need both to satisfy simultaneously.
Is that a complete list of conditions?
Will you guarantee that if the net force is zero and the net momentum is zero ...
... the solid object is in equilibrium?
Is that what physics says?
[...].