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# 1.1. Measurements in Physics

Physics is all about measuring 'stuff in the universe'. Whether that is measuring the temperature of a cup of tea cooling or the wavelength of gamma rays from a radioactive source: at the core of it, Physics is still all about measuring stuff.

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This section is mostly getting to grips with some of these key principles, as well as some terminology and conventions that we use when presenting our answers.

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I break up the chapter into the following sections, each with a brief intro about the key points, and followed up with some online videos from various sources and some quick practice questions.

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If you are confident with this stuff, skip down to Additional Resources and have a go at the summary activities.

SI Units

#### SI Units: Fundamental and Derived

The International System of Units (SI) are what we use in science as part of our aim of measuring stuff, things like Volts, Newtons, Watts are all SI units.

However, there are only 7 SI 'fundamental units':

• Mass : kilograms (kg)

• Distance : metres (m)

• Time : seconds (s)

• Current : Amps (A)

• Temperature : Kelvin (K)

• Amount : moles (mol)

• Luminosity : candela (cd)

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Everything else (e.g. Volts, Joules, mmHg) is a 'derived unit' from these 7. For example, 1 Newton = 1 kgmsË‰². Veritasium has a nice video discussing the 7 base units and how they are each defined by a universal constant. The kilogram was recently redefined, from previously being a lump of metal in Paris.

You need to be confident in converting between SI derived unit and fundamental units. Generally this involves using a variety of equations and breaking a unit up further and further until you are left with only those 7 fundamental units.

## Worked Example - the Joule

A common unit that you will be familiar with, the Joule - the unit of energy, is one example of a derived unit. So how can we work ut what a Joule is in terms of its fundamental SI units?

Firstly, let's think of some equations that make use of the Joule, or energy. One of the most common examples is Work Done. Now, let's look specifically at teh units in this equation

Now, this tells us that one Joule equals one Newton metre. Now, the metre is one of our 7 fundamental SI units, however the Newton is not. So we must keep going - let's now think of an equation involving Force.

So we have found out that one Newton is the same as one kilogram metre per second squared - going through one by one, we see that this is now all fundamental SI units. Combining these two, we can now determine that the Joule is derived as follows:

Once you're happy with that one - have a little look at trying the following for yourself. Use your formula book to help you (answers available on linked Wikipedia pages):

ii) The Pascal

iii) The Watt

iv) The Volt

v)  The Ohm

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A-Level Physics online explores this idea further in the video below.

## Video Lessons

 Cowen Physics SI and Derived Units Khan Academy Units from Formulae Khan Academy Units from Formulae Physics Online Base Units Derived Units

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Mr. G 1.1 Teaching Notes 1.1 Student Notes Physics and Maths Tutor Measurements Definitions Measurements Key Points Measurements Detailed Notes Measurements Flashcards A Level Resources - content slightly different

## Questions

 Grade Gorilla 1.1 (Measurements) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Isaac Physics SI Units Mr. G 1.1 Formative Assessment Topic 1 Summary Qs IB Specific Questions Physics and Maths Tutor Nature of Quantities 1 (OCR) Nature of Quantities 1 MS (OCR) Nature of Quantities 2 (OCR) Nature of Quantities 2 MS (OCR) A-Level Qs: overlapping content Physics and Maths Tutor MCQ Qs MCQ As A Level Physics and Maths Tutor MCQ SI & Prefixes (AQA 1) MCQ SI & Prefixes MS (AQA 1) SI & Prefixes (AQA 1) SI & Prefixes MS (AQA 1) A-Level Qs: overlapping content Physics and Maths Tutor Quantities & Units (OCR) Quantities & Units MS (OCR) A-Level Qs: overlapping content
Dimensional Analysis

#### Dimensional Analysis

This is a fancy way of we can treat units algebraically to work stuff out.

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To give a simple example, imagine I want to buy some rice that costs £2 per kilo. A Physicist shopkeeper might quote of those units as £ kgË‰¹. If I want to buy 3 kg of rice, you can probably intuitively work out that it would cost £2 kg per kilo x 3kg = £6.... But let's look at just those units.

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£ kgË‰¹         x      kg            =       £

What we've essentially done is boiled that down to just the units, and we can see that the left and right hand side are equivalent - the kilograms cancel, just as they would if they were algebraic variables.

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This same logic can be used if we break any unit down into its SI base units. The left and right hand side of equations should always remain consistent in terms of the base units. With some examples this is the units are obvious, e.g. our equation Speed = distance / time gives us:

m sË‰¹         =       m      ÷      s

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Sometimes it allows us to work out unit equivalency, e.g. Power = Energy / time allows us to show that 1 Watt is equivalent to 1 Joule per second:

W         =       J      ÷      s

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Isaac Physics have a nice section looking at dimensional analysis here. The Organic Chemistry Tutor also has produced a Khan Academy style online lesson which gives some nice examples showing how this technique can be so useful.

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## Worked Example - the Gravitational Constant

Let's take an equation you probably won't be familiar with, Newton's Law of Gravitation (we will come to it later in Section 6.2). Even though we are unfamiliar with the equation, we can use our ideas about fundamental and derived units to work out the units of our Gravitational constant.

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Q. What are the Units of the Gravitational Constant, G, in Newton's Law of Gravitation?

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We are looking to work out the units for this Gravitational Constant, G. Therefore, let's have a go at If we rearranging our equation in terms of G.

Let's now have a go at working out the units. We know we have Force in Newtons, distance in metres and mass in kilograms, giving us:

Now, we are almost there. However, the Newton is not one of our 7 fundamental units. We saw above that 1 N is equivalent to 1 kgmsË‰². We can substitute this in and simplify to give us our final units for G.

## Video Lessons

 Chris Doner Unit Conversions and Dimensional Analysis Khan Academy Dimensional Analysis Khan Academy Dimensional Analysis Physics Online Estimating Quantities

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Isaac Physics Dimensional Analysis Mr. G 1.1 Teaching Notes 1.1 Student Notes Physics and Maths Tutor Measurements Definitions Measurements Key Points Measurements Detailed Notes Measurements Flashcards A Level Resources - content slightly different

## Questions

 Dr French's Eclecticon Data Analysis Problems Data Analysis Solutions Excel Solutions Link to Dr French's Site Extension: Pre-University Material Grade Gorilla 1.1 (Measurements) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Mr. G 1.1 Formative Assessment Topic 1 Summary Qs IB Specific Questions
Significant Figures

#### Significant Figures

The number of significant figures we present an answer to is hugely important in Physics. The precision we present an value to tells us something about the precision to which we know that value to be correct.

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For example, if I say my car is 4.4 m long, that means a very different thing to saying my car is 4.382461 m long. Am I really measuring the length of my car to the nearest micron?

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To take another example. Let's say I want to find the density of a block of wood of volume 20 cm3 with a mass of 30 grams. Your calculator may tell you the density is 0.6Ë™ g cmË‰³. However, a recurring number means an infinite degree of precision - such that we are confident that our value is exactly

0.66666.... g cmË‰³.

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What this means, for IB Physics we must never present our answers as the following:

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• No recurring decimals (e.g. Ï± = 0.6Ë™  g cmË‰³)

• No fractions (e.g. x = â…– m)

• No values in terms of π (e.g. θ = 2π radians)

• No trigonometric equations (e.g. F = 3 sin 45 N)

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Significant figures become especially important when performing calculations. It's important that our final answer is presented to same precision as the least precise value used to calculate it.

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Worked Example

Q. A student is trying to measure the density of a cylinder. They measure the diameter using a micrometer to 24.03 mm. The length is measured with a ruler to be 1.2 cm. The mass is measured as 6.02 g using a mass balance. What is the density of the cylinder?

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Here we have been using various pieces of measuring equipment with different amounts of precision. To calculate density we use the equation:

Density = mass / volume

= m / πr²l

= 6.02 / (π × (2.403/ 2)² × 1.2)

= 1.1061923 ... gcmË‰³

≈ 1.1  gcmË‰³

We can only present our answer to the number of significant figures of our least precise measurements - i.e. 2 sig fig from our length measurement of 1.2 cm.

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Have a bit of practice with how to present your answers using these Isaac Physics gameboards.

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## Video Lessons

 Chris Doner Significant Figures Khan Academy Basics More Addition & Subtraction Multiplication & Division Khan Academy Basics More Addition & Subtraction Multiplication & Division Physics Online Significant Figures How many Sig Figs? Study Nova Significant Figures

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Mr. G 1.1 Teaching Notes 1.1 Student Notes Physics and Maths Tutor Measurements Definitions Measurements Key Points Measurements Detailed Notes Measurements Flashcards A Level Resources - content slightly different

## Questions

 Dr French's Eclecticon Data Analysis Problems Data Analysis Solutions Excel Solutions Link to Dr French's Site Extension: Pre-University Material Grade Gorilla 1.1 (Measurements) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Khan Academy Quick Questions Mastery Questions Mr. G 1.1 Formative Assessment Topic 1 Summary Qs IB Specific Questions
Metric Prefixes

#### Metric Prefixes

These are given to you in your formula book, but they are so important, it's definitely worth memorising the entire list from 'Giga' down to 'nano'.

We use these prefixes, as well as our standard form a lot in Physics. If you are a little rusty on these, probably worth having a bit of practice to ensure you are confident putting in prefixes and taking them out. Physics Online has a video which goes through some of these ideas.

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Spend some time converting between standard form and prefixes. They occasionally try and trip you up at GCSE with throwing in some prefixes - at IB this needs to become second nature!

Isaac Physics has a few nice problem sets, have a go at these.

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## Video Lessons

 Khan Academy Metric Unit Conversion Physics Online Unit Prefixes

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Mr. G 1.1 Teaching Notes 1.1 Student Notes Physics and Maths Tutor Measurements Definitions Measurements Key Points Measurements Detailed Notes Measurements Flashcards A Level Resources - content slightly different

## Questions

 Grade Gorilla 1.1 (Measurements) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Isaac Physics Metric Prefixes and Standard Form Converting Units Mr. G 1.1 Formative Assessment Topic 1 Summary Qs IB Specific Questions Physics and Maths Tutor MCQ SI & Prefixes (AQA 1) MCQ SI & Prefixes MS (AQA 1) SI & Prefixes (AQA 1) SI & Prefixes MS (AQA 1) A-Level Qs: overlapping content