1. Centers of Mass
Section 7.6

2. 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.

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

4. 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.

5. 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.

6. 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.

7. 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 .