James (Jim) Frankenfield - Academic Library - Physics Videos
Video #8 - Physics - Center of Mass, An Introduction
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Video #8 - Physics - An Introduction to Center of Mass
This video was done as a preliminary version of an invited lecture for an international online school. I begin by explaining center of mass and what it's good for then I solve three problems.
The first problem has a few discrete masses and we use simple sums to find the center of mass. I also present a challenge with an infinite number of discrete masses.
The second problem is a bar or rod with a linearly varying density in kg/m, so we turn our summations into integrals. Once we find the expression for the center of mass we verify it by checking that it approaches and reduces to the center for the case of a uniform density.
The third and final problem demonstrates a case in which a piece has been removed from a mass. We start with a circular disk of uniform density in kg/m2 and we remove a small circular area from it. The final center of mass is found by superposition of the two relevant centers of mass - a positive one for the solid complete disc and a negative one for the missing disc. The intention here was to find the center of mass which could serve as the location of a shaft for this part to rotate. By rotating about the center of mass we avoid problems such as rotations.
After this I provide the answer (but not a full solution) to the challenge presented earlier. Then everything is summarized.