What is the equation for calculating uncertainties in physics?

[flyboy9]

In my physics class we are constantly taking measurements and calculating uncertainty. Unfortunately my teacher has neglected to teach us how to calculate it and I am at a loss.
Currently I am working on calculating moment of inertia including its uncertainties.

Can anyone walk me through the process of how uncertainties are calculated?

Any advice is appreciated.

Thank you.

 

[HallsofIvy]

It's not clear what you are asking. You don't "calculate" the uncertainty (or error) of a measurement, it is part of the measurement itself and depends upon the method of measuring. For example, if you are measuring a distance with a ruler with marks 1 mm apart, then you give the measurement to the "nearest mm" so your error is 1/2 mm and the uncertainty is "plus or minus 1/2 mm".

If you measure two distance as, say, "20 cm plus or minus 1/2 mm" and "33 cm plus or minus 1/2 mm" then that means you distances cannot be more than 20.05 cm and 33.05 cm so their sum cannot be more than 53.1 cm. Similarly the two measurements cannot be less than 19.95 cm and 32.95 cm so their sum cannot be less than 52.9 cm. That is, the sum is "53 cm plus or minus 1 mm".

The product of those same two measurement cannot be less than 662.6525= (20)(33)+ 2.6525 cm nor less than 657.3525= (20)(33)- -2.6475. Those errors are slightly different but can be approximated by "660 plus or minus 2.65".

Notice that the "relative errors" (how large the error may be compared to the mearurement itself) are .05/20= 0.0025 and .05/33= 0.0015 while the relative error in the product is 2.65/660= .0040= .0025+ .0015.

That illustrates two engineering "rules of thumb": When adding (or subtracting) measurements, the errors add. When multiplying (or dividing) measurements, the relative errors add.

And since this is a question and not "Learning Materials", I am moving it to "General Physics"

 

[clustro]

I think he really just needs the equation for propagation of uncertainty. Its pretty straightforward. ctrl+F for "propagation of error formula"

http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc55.htm

(ignore the covariance terms.)