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2 area volume and center of mass we have already

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Unformatted text preview: ss We have already talked about area and volume in section 13.1 We will now look at Mass, Moments, and Probability Density Functions. Consider a LAMINA: A flat sheet so thin we consider it a 2D object. The density (mass/unit area) varies throughout the plate. We want to find the Mass of the Lamina. (In 101B you were able to calculate the mass of a 1D object where the density varied as you moved along the line. We know Mass = Density X Length so we chopped up the line into subintervals and created our Riemann Sum: ) In 101C, we have a 2D object, the lamina, and we will chop it up into rectangular subregions: We can get the mass exactly by taking the limit as the norm of the partition goes to zero: Mass = We want to find the Center of Mass of the lamina. This is the point where if I put a pencil tip there, the plate would balance. The center of mass is important since we can use it to simplify equations of motion and mechanics. Objects can be considered point masses located at their center of mass. Where the center of mass is loca...
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