There are a certain quantities in the Universe that are always constant.
For example, the total amount of Energy in the Universe is always constant.
Similarly, the total amount of electric charge in the Universe is always constant.
The same thing is true for two quantities which we call
“momentum” and “angular momentum.”
The speed and direction of an object is what we refer to as the object’s velocity.
The object’s velocity multiplied by its mass is the object’s momentum.
When two particles repel one another,
they each develop a momentum in opposite directions.
The sum of the momentum from the two objects cancel each other out,
so the total momentum is still zero, just as when we started.
If one of these two particles has a larger mass,
then it will move slower and have a smaller velocity.
But, because the momentum is the mass multiplied by the velocity,
the two objects will still have momentums of the exact same strength
in opposite directions, and cancel each other out.
The total momentum is therefore still zero, just as when we started.
When one object collides with another,
the momentum of one object can be transferred to another.
In this case, the green object is moving slowly,
but its momentum is large due to the fact that it has a large mass.
The total momentum is therefore the same as when we started.
Objects can have momentum in more than one direction.
The total momentum in the X direction
is the same both before and after the collision.
And the total momentum in the Y direction
is zero both before and after the collision.
The total momentum in the Universe in each dimension is conserved independently.
Now suppose that we have an object that has a momentum as shown,
and we pick any point in the universe.
The distance between this point and the object can be represented by this arrow.
This arrow and the arrow for momentum form a parallelogram.
As the object continues to move, the area of this parallelogram stays constant.
The area of this parallelogram is what we refer to as the
strength of the angular momentum around this point.
The angular momentum can be transferred from one object to another.
The angular momentum can be represented by an arrow with a direction that is
90 degrees to both of the arrows that created the parallelogram.
The length of the arrow represents the strength of the angular momentum,
which is equal to the area of the parallelogram.
Objects that are rotating around a point in opposite directions
have their arrows for angular momentum pointed in opposite directions.
In this case, as the two particles repel one another,
they each develop an angular momentum around this point, but in opposite directions.
These two angular momentums cancel each other out,
and the total angular momentum is therefore zero, just as when we started.
For any point we pick, the total angular momentum of the universe
around that point will always stay constant.
Suppose the point we pick is the center of this rotation.
In this case, the two particles have an angular momentum in the same direction,
and the total angular momentum is represented
by the sum of the areas of these two rectangles.
The angular momentum stays constant,
therefore the sum of the areas of these two rectangles stays constant.
If these two particles repel one another, the width of the rectangles will increase.
The length of the rectangles will therefore have to decrease
to keep the area of the rectangles constant.
This means that the velocity of the particles will have to decrease,
and rotation will have to slow down, so as to keep the total angular momentum constant.
On the other hand, if these two particles attract one another,
then the velocity of the particles will have to increase,
so as to keep the area of the rectangles constant,
and hence keep the total angular momentum constant.
The linear momentum is also conserved,
since we started out with a total linear momentum of zero,
and we ended up with a total linear momentum of zero.
Much more detailed information about this is available in the video titled,
“Torque, Levers, and the Universal Law of Rotation”,
and in the other videos on this channel.
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