Find the mass and the coordinates for the center of mass of a thin wire formed like a quarter circle.
Circle equation: x2+y2=r2
Mass density: rho=x+y
The Attempt at a Solution
I know that: x2+y2=cos2(t)+sin2(t)=1
This leads to: x2+y2=r2(cos2(t)+sin2(t))=r2
The quarter circle is described by the vector equation:
The density function becomes:
The line integral that I try to use: (C is the quarter circle wire)
This ends up in M=0.... FFFUUUU! The right answer is supposed to be 2r2
I can't seem to find the right solution to this... please help.