The center of mass is often times called the center of gravity. The center of mass is also known as the point of an objects positional mass.
Let's talk about the center of mass, this is often times called the center of gravity as well the only time these two aren't the same is if something is really really really tall like a really really tall building because remember gravity is inversely proportional to the distance between the two objects so if you had a really tall building the gravity would be weaker further from the earth than closer to the ground but for everyday objects, even tall buildings in in cities around here center of gravity, center of mass are about the same and what they are basically is the point of an object's average positional mass so if you take an object and you can get it to balance whatever that point is that it balances, is the center of mass pretty straight forward.
So for a ball, if I take a ball and I throw it and it's spinning it's going to spin probably around somewhere here in the center that's pretty easy right? Now let's say if I took this bat and I threw it so that it was moving and spinning around itself, it would spin around its center of mass too but center of mass with this bat, because I've got more mass up here, would probably be up in this area okay? And that would be the center of mass upon which the bat continue to rotate okay?
For a triangle, remember in Geometry, the center of mass if I have the height of the triangle h it's going to be h divided by 3 which will, pretty made it a little too big there, h would probably be right about there okay so the center of mass will probably be right about there okay.
For a cone, the center of mass is going to be again if I have this is h it's going to be h divided by 4 which will put it up right about there.
There are some objects that have a center of mass outside of the object, well how can that happen? Well if I have a boomerang if you ever notice boomerangs when they rotate around their center of mass, their center of mass is outside of the actual object so that can actually happen that happens often times in systems.
Also sometimes when you look at stars in in other galaxies, astronomers can actually that they have planets around them, we can't see planets, planets don't produce any light, how can you tell that there's a planet there? Well that's because they can see the star wobbling. And why would the star wobble? Well again, the star and its planets make up a system or a unit that's rotating around its center of mass so if there are large planets around the star, then the center of mass will not be in the star itself, it will be somewhere outside that and you'll see the star wobble, that movement of the star is due to a center of mass outside of the actual star, so this is some examples of centers of mass and why different objects then have different types of center of mass.
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