Now we're gonna move to the center of mass.
The idea of center of mass is just to ask where would an object balance.
In other words, where could I put my finger or put a string
that's holding the object so that the object would be perfectly balanced at that point.
If I, for example, took an object like this one and hang it from a string,
I can draw a dotted line down exactly in the line of the string itself.
If I then hang the object from a different point maybe from the side
I could repeat and also draw a dotted line,
the place where this dotted line meet would be the center of mass of the object.
At this particular point on the object if you balance it perfectly on your finger
or another object and be very careful it would stay perfectly balanced,
meaning that mass is equally distributed about that point because it is by definition the center of mass.
The center of mass is important because for any object
anything you consider you can find the center of mass of that object including for a person.
So as a person, grows and ages and changes how they walk and their posture
the center of mass of that person can also change where its location is
and has a very important ramifications for the mechanics of the body
and how the body works and has to come as using its muscle
depending on where a person's center of mass is.
It's also important to notice that the center of mass does not necessarily need to be inside the object itself.
So for example, if you consider somebody hunch over like this
if they're bend like this the center of mass can be actually be residing outside the person,
because the center of mass is not talking about our location within the mass,
the center of mass is trying to tell you where the mass is equally distributed around
and that can again be outside of the object itself.
Let's do a quick pictorial, representation of center of mass,
supposed we have two point objects like this and we're just considering one dimension along the x direction,
where x is equal zero and then goes off to the side.
One mass is much bigger than the other
and we could expect just by intuition of the center of mass of the system of two masses,
would be somewhere in between but more towards the heavier mass.
The way to find this mathematically, is to multiply the masses
times the position of the objects and then to divide it by the total mass of your system.
So if you look at the numerator of this expression we have mass 1
times its position plus mass 2 times its position and if we have more masses we would keep going.
But, if we just lifted it at that way, we would have units of mass times position, and that's not a good location.
For location we need units of distance, and so we have to divide it by the masses at the end.
What we're doing here conceptionally, is we're giving each position X1 and X2 etc.
It's on weight per see we're sort of biasing the center of mass towards heavier objects.
So in other words, X1 here gets more of a say more of a weight toward its position
because it has a large mass located at X1.
And then at the end of the day again we divide it by the total mass
so that we end up with units of just position.