Now, all the course notes/ books I read says this must be converted in radians, even though the angle we use here is measured in degree. Anybody can ask a question

Errors are mistakes in the readings that, had the experiment been done differently, been avoided.

write (30 ± 1)º. By clicking “Post Your Answer”, you agree to our To subscribe to this RSS feed, copy and paste this URL into your RSS reader. It only takes a minute to sign up.I wonder why uncertainties in angle measurement MUST be in radians.

The uncertainty of a measuring instrument is estimated as plus or minus (±) half the smallest scale division. For example, if you took an angle measurement: q = 25°± 1° and you needed to find f = cosq, then f max = cos(26°) = 0.8988 f min = cos(24°) = 0.9135 \f » 0.906 ±0.007 Note that even though q was only measured to 2 significant figures, f is known to 3 figures.

(See the section on dealing with averages below). There are two rules of thumb:Firstly, take repeat readings. Unfortunately it is not always possible to know when you are making an error (otherwise you wouldn't make it!) They don't have to be. So in the example above: Relative uncertainty = (0.2 cm ÷ 3.4 cm) × 100% = 5.9%. Stack Exchange network consists of 176 Q&A communities including

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If the experiment generates many repeat readings (as any really good experiment should) then there is a way to analyse the results and obtain a good value for the associated uncertainty: Take an … How come?Because, if you don't use radians the derivative of $\sin\theta$ is not $\cos\theta$, and so your formula $dy=\cos\theta\,d\theta$ doesn't hold (it needs a coefficient). Mathematics Stack Exchange works best with JavaScript enabled It is just if you don't you will have a bunch of $\frac{\pi}{180}$ factors when you differentiate $\sin \frac{\pi x}{180}$ which is the expression for $\sin$ in degrees. For example, I want to calculate the uncertainty in measuring the function y = sin (θ) when the angle is measured θ = 63 ± 1 degree. Detailed answers to any questions you might have Work this out with: Relative uncertainty = (absolute uncertainty ÷ best estimate) × 100%. What you are doing in effect is seeing how repeatable the results are and this will give an order of magnitude idea of the uncertainty likely on any given reading. that make sense, I didn't think I have to convert the angle in radians anyway when I differentiate.

The uncertainty is taken as 4sSecondly, if the results are repeatable to the precision of the measuring apparatus then the uncertainty is taken as half of the smallest reading possible.

The relative uncertainty gives the uncertainty as a percentage of the original value. The values on the x-axis are shown with a constant absolute uncertainty, the values on the y-axis are shown with a percentage uncertainty (and so the error bars gets bigger)The art of analysing experimental data is knowing what to plot, in most experiments it is not enough to simply plot the recorded values directly, instead some more appropriate graph is needed.



Average values. The mathematical relationship for a linear relationship is y = mx + cIn a Physical situation each of these quantities has physical meaning and appropriate units - this includes the gradient and the y-intercept. Consider our previous example:In all of the following examples we consider combing 2 values:Having taken measurements and calculated the associated uncertainties, it is often necessary to plot these values graphically. For example, I want to calculate the uncertainty in measuring the function $y= \sin (\theta)$ when the angle is measured $\theta = 63$ $\pm 1$ degree. By using our site, you acknowledge that you have read and understand our Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

Thank you!



I do this using differential, so $dy = \cos (\theta) d\theta$, now $d\theta = \pm 1$ degree is the error in $\theta$. The same result follows for the combined standard uncertainty of the remaining angle deviation estimates. Don't forget to include units when calculating values from a 'Physics' graph!

I do this using differential, so d …

Error bars are simply a line used to represent the possible range of values, the line or curve drawn through the points can pass through any part of the error bar. Uncertainty cannot be avoided but it can be reduced by using 'better' apparatus.

For example, when measuring something with a ruler marked off in mm, the uncertainty is ± 0.5mm.


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