Center of Mass via Scalar Line Integrals

[Hashmeer]

Homework Statement

A thin wire has the shape of the first quadrant part of the circle with center at the origin and radius a. If the density function is rho(x,y)=kxy, find the mass and center of mass of the wire.

Homework Equations

My parametric equation of the circle was x=a*cos(t) and y=a*sin(t).

The Attempt at a Solution

I really have no clue where to begin for finding the center of mass of the wire. I think I got the mass via integral(k*a^2*sin(t)*cos(t) dt = -(k*a^2)/2. Thanks for the help!

 

[tiny-tim]

Hi Hashmeer!

(try using the X² tag just above the Reply box )

… I think I got the mass via integral(k*a^2*sin(t)*cos(t) dt = -(k*a^2)/2.

No, mass = ∫ density*d(length),

and d(length) is not dt, it's … ?

 

[Hashmeer]

Yea, I looked over my notes and I figured out what I need to do. Thanks for confirming what I was thinking was wrong.