How to Determine the Center of Mass

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Determining the center of mass will require you to take some very specific measurements. Determine the center of mass with help from an experienced math professional in this free video clip.

Part of the Video Series: Solving Math Problems
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Hi, I'm Ryan Ault. I'm a physicist, and this is how to determine the center of mass. If your system is composed of two different particle, and a line connects the two, you can label each with a mass. This has m1, your second particle has m2, and we can say that m1 is positioned at x1, and m2 is positioned at x2. Now the equation for center of mass in the x direction is simply Xcm is equal to the summation from i equals 1 to n, total number of particles, and inside of this summation for each particle, for instance looking at particle one, we want to take particles, the particles mass and we want to multiply by the particles position, and once we've done this for all particles, the summation, we want to divide by the total mass. And in this example above, we find that the center of mass is equal to m1x1 plus m2x2, divided by m1 plus m2. Now this equation looks slightly foreign possibly, and in order to test its validity, think about just one particle being here. If we set m2 equal to zero, it's kind of like m1 existing only by itself. So if we do set m2 to zero, this term would go to zero, this one would go to zero, and we find the x center of mass is m1x1 over m1, which simply reduces to x1. So we know this equation is valid for this two particle system above. I'm Ryan Ault, this is how to determine the enter of mass.

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