Why is the uncertaintiy on a cm ruler and a metre ruler the same? PHYSICS help!

I believe you are referring to a metre rule, not metre ruler. See from the image that the precision is 1mm. With a metre rule, the physical ends of it are literally 0cm and 100cm as you can see in this image:



Thus when you place it against an object, one end of the rule (0cm) is already aligned with the end of what you are measuring. There is 0 uncertainty here. The other end of the object is somewhere along the rule. This means the total uncertainty is 0 + (+-)0.5mm = +-0.5mm


With a 30cm ruler, the end does not necessarily (and in most cases is assumed not to) start at 0cm. As you can see in this image, the end of the ruler is not actually 0cm. 0cm appears slightly inwards from the physical edge of the ruler.
Now when we measure an object with a ruler, we place one end of the object at the 0cm marker on the ruler. However since it is not at the physical edge and so we cannot be certain when aligning it, there is a +-0.5mm uncertainty here. And at the other end of the object (which falls somewhere along the ruler), there is the usual +-0.5mm uncertainty which we also saw on the metre rule.

The total uncertainty here is +-0.5mm + +-0.5mm = +-1mm

Okay This helped loads! So I understood this (i hope) and I sort of combined this with things I already know. My understanding (correct me if i'm wrong)

With a ruler... or any other form of analogue measurement...
The uncertainty is given as half the smallest division of that instrument. So for a cm ruler, it increments in 1 mm each time. Thus half of 1mm is 0.5mm. So our uncertainty is +/- 0.5mm. However because the ruler must be placed so that the object is aligned at zero, there is an additional +/-0.5mm error. So the total error is +/- 1mm for a cm ruler.

For a metre rule, since it starts exactly at zero and is placed exactly on the object, there is no error at the start, but there is a +/- 0.5mm error at the end (since it increments in 1mm /2 = 0.5mm)

This is the part I don't understand:
For a mm ruler... It increments in 1mm each time (since this is the smallest), so half the smallest division thus +/- 0.5mm each time. Now apparently this is the uncertainty? But what about the error at the start of the ruler for a mm ruler? Is there not a +/- 0.5mm error there too? Shouldn't the error on a mm ruler be 1mm too (like the cm ruler? )

Your understanding is exactly right! So glad you get it

About your question - What's a mm ruler?

Kill me. *hides face in shame*

Haha dw xD Were you referring to a metre rule?

unfortunately not :/ I thought it existed lmao

But one more thing
According to Google, the uncertainty of a metre rule is 1mm, not 0.5mm?
Apparently the uncertainty is +/- 1mm but I don't know how they got that
Also, what if it was a metre rule that only incremented in cm? 1cm/2 = 0.5cm = +/- 5mm? is this correct?

I don't think Google is right there. Unless they're talking about a metre ruler. The uncertainty can be written as either 1mm or +- 0.5mm. It's the same thing.

I've never seen those except in primary school classrooms, but yes you would be correct there

Well Student403 > Google I think xD
Is there anything else that I'm missing about the underlying principles of uncertainties for A level Physics or is that about it?
Thanks a bunch for your help!

Haha no I'm just telling you what my teacher's taught us for the past two years xD (I only trust him cause he's an Edexcel examiner)

I really liked this document for revising uncertainties.

http://web.uvic.ca/~jalexndr/192UncertRules.pdf

All the best

(For Edexcel at least, you don't need to remember the delta and epsilon symbols)

That's a great resource! Thanks!
Just to clarify: does the same apply to digital scales i.e. a multimeter?
I watched a few videos and it seems that they just take the "smallest division" I.e. what the scale increments by, without dividing it by two. Is this correct?

Good question. I'm a bit scratchy on this myself so do clarify with your physics teacher. But from what I remember, yes the uncertainty is the smallest division or plus/minus half the smallest division. (Remember there are two ways of writing uncertainty).

However when, for example with a voltmeter, you connect it to two ends, it might be different. Do check this

Okay, I think this video is causing a bit of confusion now xD
https://www.youtube.com/watch?v=MwzDPhV6dlY&list=PLlDtVvefFYT-LUGAGJ1aL-mwE4ngGhN7M&index=3

When he's measuring using the ruler he takes a +/- 0.5mm error at the start... I don't understand why since the ruler starts exactly at zero as with a metre rule?
Okay theres a comment on this lol
question: Is there always uncertainty at the start of a measurement?
answer: Excellent question (and one that is still very much open to debate). The latest info I received directly from the exam board is that for a digital instrument then there isn't an error at the start of the measurement


Also if you skip ahead to where he pulls out the digital caliper, he has an error of +/- 0.01 mm. I understand that the digital caliper increments by 0.01mm, so shouldn't the uncertainty read +/- 0.005 mm? Okay wait, in the comments section someone asks about this.
question:
But why if the voltmeter and stopwatch can read 0.01 is the uncertainty 0.01? Shouldn't it be 0.005? I don't understand, is the uncertainty just the smallest measurement then?

answer: My understanding (especially based on the way the OCR look at uncertainties) is that for an analogue scale the uncertainty is to half the smallest scale division which in the case of a ruler is +/- 0.5 mm at each end so +/-1mm like you said. For a digital scale the uncertainty is the smallest scale division on the measuring instrument. That's the guidance I was given when I queried this with the exam board and that is what they are expecting students to use.


Sorry about this... Maybe I'm picking from too many sources xD I do AQA and the video is customised to OCR. :/ how do i find out what AQA wants? My Physics teacher is a bit of a round about person.. he'll tell you a bunch of stuff and somehow manage to avoid answering the question xD


EDIT: Nope wait, I have a handbook from AQA that I foudn online, it reads:
When measuring length two uncertainties must be included. The uncertainty of the placement of zero of the ruler adn the uncertaintity of the point the measurement is taken from. As both endes of the ruler have a +/- 0.5 scale division uncertainty the measurement will have an uncertainty of +/- 1 division. For most rulers this will mean it has an uncertainty of +/1 division.
Sorry to trouble you! Found the answers...

To summarise:
For AQA, theres always a +/- 0.5 scale division uncertainty at the beginning as well. I assume this applies for a metre rule too.
With regards to digital tools, AQA's handbook doesnt say anything on this BUT, it does say: "Measurement are often written with the uncertainty. An example of this would be to write a voltage was (2.40 +/- 0.005) V. So they half the uncertainty? Not entirely clear on this but I will ask my teacher

Well Student403 > Google I think xD
Is there anything else that I'm missing about the underlying principles of uncertainties for A level Physics or is that about it?
Thanks a bunch for your help!