# Center of Mas of a planar Lamina

1. Jul 24, 2014

### hagobarcos

1. The problem statement, all variables and given/known data

Find the center of mass of a planar lamina, in the form of a triangle with vertices (0,0),(0,a),(a,a),
if ρ=k

2. Relevant equations

m = ∫∫f dA

xbar = My/m

ybar = Mx/m

3. The attempt at a solution

mass = ka²/2

Mx = ∫∫yk dy dx

My = ∫∫xk dy dx

**Side Question, how do we use math type or some other type of symbolic language on physics forums? ***

Any thoughts would be appreciated.
Below is my photo:

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2. Jul 25, 2014

### Simon Bridge

You can use LaTeX to type maths.
i.e. $$M_x = \iint ky\;dy\;dx$$

Did you have a question?

3. Jul 25, 2014

### HallsofIvy

Staff Emeritus
If the density is a constant, the "center of mass" is the "centroid", the geometric center of the figure. And for a triangle that is particularly simple to find. If you really want to use the double integral, x goes from 0 to a and, for each x, y goes from 0 to x:

$$m= \int_0^a\int_0^x k dydx$$
$$M_x= \int_0^a\int_0^x kx dydx$$
$$M_y= \int_0^a\int_0^x ky dydx$$

4. Jul 25, 2014

### hagobarcos

Aw sweet, turns out I had the wrong variable in my Mx & My formulas, kept getting the thing wrong:)

And for symbols, my screen just shows "quick symbols", none of the fancy LaTex y'all are using ^^

5. Jul 25, 2014

### hagobarcos

Okay actually I do have a question, in my book the formula for Mx is double integral of ky dA

And for My is double integral kx dA

Which is correct?

6. Jul 26, 2014

### HallsofIvy

Staff Emeritus
What do you mean "which" is correct? $M_x$ is the moment of inertia about the x axis and is $\int\int ky dA$. The y coordinate of the center of mass is $\overline{y}= M_x/m= \int\int ky dA/m$ and the x coordinate of the center of mass is $\overline{x}= M_y/m= \int\int kx dA/m$.

Personally, I find the "$M_x$", "$M_y$" notation "non-intuitive" and prefer the $\overline{x}= \int\int kx dA$, $\overline{y}= \int\int ky dA$ notation.

7. Jul 28, 2014

### hagobarcos

oh!! Yes :D Excellent, thank you for clearing that up.