Center of mass and center of gravity are two terms that are often used interchangeably, but they're really not the same.
Let's take an object, like, for example, a 5 kilogram bowling ball. If you drop a bowling ball, it will fall to the ground because of the force of gravity. But did you know that the bowling ball will fall to the ground in the same way that a 5 kilogram point mass would if the point mass was placed at the very center of the bowling ball?
The bowling ball is a uniform object with a center of mass at the very center of the bowling ball. The center of mass is the mean position of the mass in an object. If you have the same amount of mass to your right as you have to your left and the same amount above as you have below and the same amount in front as you have behind, then you must be at the center of mass.
The bowling ball also has a center of gravity, which is the point where gravity appears to act. Or in other words, it's the sum total of all the forces of gravity on all the particles in the object. It doesn't take much understanding of physics to realize that for the bowling ball, this is also at the very center of the object. For the bowling ball, the center of mass and center of gravity are pretty much in the same place.
But they're NOT the same thing. It turns out that they're only the same when the gravitational field is uniform across the object, or at least close enough to be uniform that it isn't worth discussing. With small objects near the surface of the Earth, that's always the case. But once you start putting spaceships in space, suddenly things get weird.
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Let's go through a couple of examples of when the center of mass and center of gravity are not the same. We'll start off with a super abstract example.
One day, you buy a really large aluminum bar. Because you have nothing better to do with your money. This bar is HUGE. It's as tall as you are, just as deep, and it's 100 miles wide. I told you it was huge!
You position this bar on a stand, such that the longest side of the cuboid is at 90 degrees to the radius of the Earth. In this situation, the center of mass and center of gravity of the cuboid is not the same. Here's why.
We like to think of the Earth's gravitational field strength as being a nice constant of 9.8 m/s/s. But that's not actually true. That's the average value at the surface of the Earth. But as you get further and further away from the Earth, gravity gets gradually weaker. Not a lot at first, just a bit. But it does change. On Mount Everest, for example, the acceleration due to gravity is more like 9.75 m/s/s.
So anyway, if you have a huge metal bar, the center of the bar will be closer to the center of the Earth than the outside of the bar. Remember that the Earth is round (or an oblate spheroid to be exact). So the two edges will be further away from the center of the earth and experience weaker gravity. The center of mass of the bar is still right in the center, but because of this variation in gravitational field strength, the center of gravity, the place where gravity appears to act, ends up being a little higher - a little further from the center of the Earth.
A more practical example of this would be the International Space Station. Once you start getting out into space, these differences in gravitational field strength become a lot more pronounced. For NASA or for the ESA (or whatever your favorite space agency happens to be), the difference between center of gravity and center of mass is all too important. Fail to take it into account, and you could send your spaceship crashing into the Earth.
Center of mass and center of gravity are two terms that are often used interchangeably, but they're really not the same. The center of mass is the mean position of the mass in an object. Then there's the center of gravity, which is the point where gravity appears to act. For many objects, these two points are in exactly the same place. But they're only the same when the gravitational field is uniform across an object. For larger objects or objects in orbit, that isn't always the case.
If you have a huge metal bar that is positioned at 90 degrees to the Earth's radius, the center of the bar will be closer to the center of the Earth than the outside of the bar. Because of the variation in gravitational field strength this brings, the center of gravity, the place where gravity appears to act, ends up being a little higher - a little further from the center of the Earth - than the center of mass.
The difference between center of mass and center of gravity becomes really important when you're putting objects and people into space. Fail to take it into account and your spaceship won't do what you expect at all.
After you have finished this lesson you should be able to explain the difference between an object's center of gravity and its center of mass.
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The center of mass and center of gravity are closely related. An extended object or cluster of point masses has a location within or around it where all of the mass of the system can be thought of as being concentrated; the system's center of gravity is where the force of gravity acts on an object.
When it comes to physics, you can't do enough practice. Very little has to be memorized in physics because it would be very difficult and inefficient to memorize every scenario possible. In fact, it might be impossible! That said, here are some more practice problems to help you apply the center of mass and center of gravity concepts.
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