(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the mass and the coordinates for the center of mass of a thin wire formed like a quarter circle.

2. Relevant equations

Circle equation: x^{2}+y^{2}=r^{2}

Mass density: rho=x+y

3. The attempt at a solution

I know that: x^{2}+y^{2}=cos^{2}(t)+sin^{2}(t)=1

This leads to: x^{2}+y^{2}=r^{2}(cos^{2}(t)+sin^{2}(t))=r^{2}

x=r*cos(t)

y=r*sin(t)

The quarter circle is described by the vector equation:

r(t)=r*cos(t)i+r*sin(t)j; 0<t<1/2*pi

The density function becomes:

rho=x+y=r*cos(t)+r*sin(t)=r(cos(t)+sin(t))

The line integral that I try to use: (C is the quarter circle wire)

M=∫[itex]_{C}[/itex](rho(x,y)*ds)=∫[itex]^{1/2*pi}_{0}[/itex](rho(x,y)*r'(t)*dt)

=r^{2}∫[itex]^{1/2*pi}_{0}[/itex](cos^{2}(t)-sin^{2}(t))*dt

This ends up in M=0.... FFFUUUU! The right answer is supposed to be 2r^{2}

I can't seem to find the right solution to this... please help.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Mass of 2 dimensional object - line integral

**Physics Forums | Science Articles, Homework Help, Discussion**