Finding the CM of a Bar of Variable Density

  • #1

Homework Statement

We are given a bar, with length of [tex]d[/tex], and it's densitiy is given by this formula: [tex]\lambda=\lambda_{0}+2ax[/tex], where x is the distance from one side of the bar and a is a constant

Homework Equations

[tex]\vec{r}_{CM}=\frac{\sum\vec{r}_{i}\Delta m_{i}}{m}[/tex]

The Attempt at a Solution

Well, I figured, if I have infinitesimal parts of the bar, I should integrate it.
So, this is what I've come up with so far:


  • #2
Where is the question? Your formulas look ok.
  • #3
Well, I was not sure of this because the solution looks very awful, and I had no one to verify this.
But if it seems OK to you, I guess it's correct then.
  • #4
Well the math works out correctly, although you can pull a 'd' out from the numerator to slightly simplify it a bit more. Unless you misread something, then everything looks correct.

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