Understanding the Center of Mass & Center of Gravity

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• 0:02 Center of Mass vs.…
• 1:38 Examples
• 3:40 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you will be able to explain the difference between center of mass and center of gravity and give examples of situations where they would be different. A short quiz will follow.

Center of Mass vs. Center of Gravity

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.

Examples

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.

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