Error Propagation for F=4*pi^2*r*m/T^2

[badtwistoffate]

I know there is a formulas for doing error propagation with separate formulas for when dealing with powers, multiplying/dividing, and adding/subtraction.
What about if I have the formula F=4*pi^2*r*m / T^2...?
Also should i do error propagation for the varibles in the formula r (radius), and T(Period).

 

[big man]

If the variables in your formula r,m and T each have an associated uncertainty then you take into account their affect on the final result F.
I'm pretty useless with the Latex and it is just easier and faster to do it in word so I've explained what I've done in the attached document instead.
I'm sorry if I've explained stuff you already know, but like I said, I don't really have an idea of what you know already so I thought I'd cover all bases.

 

[badtwistoffate]

why can't i download it?

 

[big man]

Yeah sorry forgot about the pending approval thing so you can't see it until a mod approves it, but yeah I can just send it to you if you want.

 

[badtwistoffate]

can you send it to etownsen@oswego.edu
thanks

 

[big man]

done.

If you don't really follow it then just come back here to discuss it and I will try and clarify it...or someone else will.

 

[badtwistoffate]

Um with eqn 2, in the square root, After the (uncertainty in f / uncertainty in m) squared, is that then times the standard deviation of m squared? Also in ours m, has no uncertainty so we just leave that term out of eqn 1?

 

[big man]

Yeah if it has no error associated with its value then it doesn't contribute to the error in the final value.
The $$\sigma_m$$ is just the uncertainty associated with the value m.
However, since you are given the value of m and it doesn't have an uncertainty then you will just leave it out of the expression. Remember that you only include the expressions that have an associated uncertainty.

 

[badtwistoffate]

Also, could you try explaining this part again? So for the partial derivative (uncertainty in F/uncertainty in r ) we treat the variables m and T as constants while differentiating F with respect to r. so the partial derivative is just the equation without r? And we sub this into the partial derivative spot? Do we sub those numbers in too?

 

[big man]

To answer your question about the partial derivative, yes it will just become the equation without r in it. Once you have the partial derivative expression you substitute in your known values for T and m into the expression. Then square the expression and multiply by the square of the uncertainty in r. By the way the partial derivative symbol that I used isn't uncertainty in F/uncertainty in r. It is essentially dF/dr...the symbol just tells you that it is the partial derivative.