Centers of Mass Section 7.6.

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Presentation transcript:

Centers of Mass Section 7.6

Centers of Mass Find the center of mass of the system with point masses 𝑚 1 =5, 𝑚 2 =6, 𝑚 3 =12 located at (4, -1), (0,0) and (-3, 5) respectively.

New Vocab and Formulas Lamina: A thin sheet of material of constant density Density: 𝐷= 𝑚 𝑉 or 𝐷= 𝑚 𝐴

Centers of Mass Find the center of mass of the lamina of uniform density ρ bounded by the graph of 𝑓 𝑥 =4− 𝑥 2 and the x-axis.

Center of Mass Find the center of mass of the region bounded by the graphs of 𝑓 𝑥 =4− 𝑥 2 and 𝑔 𝑥 =𝑥+2. Density is a constant ρ.

Center of Mass Find the center of mass of the region bounded by the parabolas 𝑦= 𝑥 2 −3 and 𝑦=−2 𝑥 2 . Density is a constant ρ.

CHALLENGE!!! Find the center of mass of the region with constant density bound by the graph of 𝑦=9− 𝑥 2 and the x-axis. Density at a point (x, y) can be defined by the equation ρ=2 𝑥 2 .