Calculate the moments M_y and M_x and the center of mass of a lamina with density p=1 bounded by the curves y = 5 -|x| and y = 1 + |x|.

Question

I'm a bit confused on how to start this problem. Thank you for any help you can give me.

Answer 1

You can do a lot of integrating to solve this, but it is pretty easy to see that x = 0 and y = 3 are axes of symmetry, so the centroid is at (0, 3)

To show: Because x only appears as |x|, the function is symmetric about x = 0.

As (5 - |x|) - 3 = 2 - |x|, and 3 - (1 + |x|) = 2 - |x|, the 2 y functions are equidistant from y = 3.