How can I find out the center of mass of thin plate in the shape of a rectangle ABCD
If the density at any point is the product of the distances of the point from two adjacent
sides AB and AD? (Assuming that AB and AD are alongside of X-axis and Y-axis respectively.
I think to find out center of mass, we need to evaluate double integral.
$$\hat{x}=\frac{\int\int xf(x,y)dx dy\cdot}{\text{Total Mass}}.$$
In this question, how can I find general form of density function and total mass?
Best Answer
You are told that the density is the product of the distances from AB and AD, so $f(x,y)=xy$ is your density. Then the total mass is $\int \int xy \ dx \ dy $ over the rectangle.