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Understanding the Center of Mass & Center of Gravity

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.

Expert Contributor
Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education. He has taught high school chemistry and physics for 14 years.

The center of mass and the center of gravity may not always be equal, and this can have important implications. Learn how to determine the center of mass vs. the center of gravity, and review examples demonstrating that an object's center of mass and its center of gravity are not the same. Updated: 10/31/2021

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.

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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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Center of Mass Calculations

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.

Practice Problems

1. Imagine there are three spheres of equal mass positioned at the vertices of an equilateral triangle. Where is the center of mass of this system located?
2. Would the center of mass or gravity of the three masses in problem 1 be in a different location if it were on the Moon versus on Earth? Why or why not?
3. Imagine having a 1-meter long rod of aluminum that tapered from a 1-cm diameter on one end and a 5-cm diameter on the other end. Roughly describe the location of the center of the mass of the rod.
4. Gravity is involved in the center of gravity concept. What happens to the gravitational field as the distance from the surface of a planet increases?
5. Describe a scenario where the center of mass and center of gravity are not in the same location.

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