l1 dimensions and scalars

8/2/2019 L1 Dimensions and Scalars

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Dimension and Units

At the end of this lecture you should:

Understandwhat a physical dimensionis and what physicalunitsare and the correspondence between them in the SIsystem.

Knowwhat the baseSI units are and what they measure.

Knowthe difference between a base unitand a derived unit.

Be able tocheck whether an equation is homogenous ornot.

Be able tomake an educated guess at a physicalrelationship between variables, based on whether theequation is homogenous or not.

Havenotes from this lecture that are legible and useful


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Short introduction

At the end of the year, your certificate fromthe CPS will give you a percentage (%) inphysics only.

Mark division:

Exams: Xmas 5% Easter 5% Final 60%

Course work tests: 10% Practical: Project 5% Laboratory work 15%


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Lectures (about 46 in total)

Lectures: same lecture roomall year.

You must sign the registerduring the lecture. Please do

this quietly and efficientlythank you.


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Problem Solving Classes (PSC)

Two per week Bring your notes from the lecture; bring

pen, notebook, ruler and calculator.

This is the time to ask your teacherquestions and clarify yourunderstanding.

Initially,16 PSC groups. Soon, there willbe 20 PSC groups (when a new teacher

is here)


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Projects

Projects will start in teaching weektwo on Tuesday afternoon. Projectswill be done in groups and we will

decide who works together. Projectsstart in teaching week two and will be

completed by Monday of teaching

week eight; i.e. Monday November

21.


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Laboratory work

In total, student do 7 or 8experiments. During teachingweeks 8 and 9, students will do their

first laboratory experiment. Theseexperiments will continue in term

two and term three. Experimentswill be on Tuesday, Thursday andFriday afternoons. Students work in

pairs.


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Courseworks (CWs)

Distributed every week on Thursday.Questions in CWs and PSCs will betested.

2 pm, Tuesday October 17 test on CWs 1-2 2 pm, Tuesday October 31 test on CWs 3-4

2 pm, Tuesday November 28 test on CWs

5-7


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Questions? More information will be uploaded onto Moodle this

week. If you have any urgent specific question, write to the

Physics Coordinator, Steve before Wednesday 6 pm thisweek. Steve will upload to Moodle answers to thesequestions by Friday this week.

[email protected]

Give your email the title: Question about physics. Start

the email either Dear Steve or Hi Steve End your

email something like Thanks and best wishes and

always write your name.

Generally, if you have any question about the physicsteaching, the physics teachers, etc which you do not feelyou want to ask your PSC teacher directly, please write

to Steve.
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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CPS Physics Lecture 1

Dimensions and

Units


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Oxford English dictionary: Physics is the

science dealing with properties and interactionsof matter and energy.

Wikipedia states: Physics (from the Greek,

(physikos), "natural", and (physis), "Nature") is the science of the naturalworld. It deals with the fundamental constituentsof the universe, the forces they exert on one

another, and the results produced by theseforces.
http://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Sciencehttp://en.wikipedia.org/wiki/Naturehttp://en.wikipedia.org/wiki/Naturehttp://en.wikipedia.org/wiki/Universehttp://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Universehttp://en.wikipedia.org/wiki/Naturehttp://en.wikipedia.org/wiki/Naturehttp://en.wikipedia.org/wiki/Sciencehttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Physics


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Another important view, the atomic hypothesis:

Richard Feynman: All things are made of atoms little particles that move around in perpetual

motion, attracting each other when they are alittle distance apart and repelling on beingsqueezed together.

(Go NU library to read: The Feynmann Lectures

on Physics, Volumes I-III. This is challenging butexcellent for your English and very interesting ifyou like physics! Also, all lectures are availableonline: )


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Yet another view is Einsteins.

E = mc2

where E is energy, m is mass of matterand c is the speed of light (radiation).

In summary, we can say: Physics studiesmatter, forces and energy all of whichare closely linked.


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Units

Physics is quantitative. We can askhow much or how long, how fast orhow hot, etc.

So, we need ways to measurethevariables we are working with.

Note this quantitative aspect together

with that of theory allows us to predictthe behaviour of the phenomena in theworld.

This makes physics POWERFUL.


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Dimensions and Units

Physicists think that the world iscomprised of different types ofquantities: dimensions. The

seven dimensions are:Physical

Quantity

SI unit Dimension


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Until now, all quantities in nature have

units that are a combination of theseseven base unitsand two additional units,namely radianand steradian.

Base unitsare defined using somestandard or easily reproduciblephenomenon.

E.g., 1 kg is a lump of matter in Paris

E.g., 1 s is 9,192,631,770 jumps of anelectron between two energy shells incaesium 133.


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International Bureau of Weights and Measures in Svres,France


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Caesium atomic clock in Switzerland with anuncertainty of one second in 30 million years


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Expressing answers correctly

All physical quantities are expressedas a number followed by thecorresponding unit:

Physical quantity = number x unitE.g., A distance of about half akilometre = 521 m or 0.521 km

E.g., The acceleration due to earthsgravity = 9.81 m s-2


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Example 1

Find a Newton (N) in terms of

(i.t.o) base units.

Note The Newton is a derivedunit. Other examples of derivedunits are:


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Prefix Symbol 10n

giga G 109

mega M 106

kilo k 103

milli m 103

micro 106nano n 109

Prefixes that you are expected to know
http://en.wikipedia.org/wiki/Giga-http://en.wikipedia.org/wiki/1000000000_(number)http://en.wikipedia.org/wiki/1000000000_(number)http://en.wikipedia.org/wiki/Mega-http://en.wikipedia.org/wiki/1000000_(number)http://en.wikipedia.org/wiki/1000000_(number)http://en.wikipedia.org/wiki/Kilo-http://en.wikipedia.org/wiki/1000_(number)http://en.wikipedia.org/wiki/1000_(number)http://en.wikipedia.org/wiki/Milli-http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Micro-http://en.wikipedia.org/wiki/Mu_(letter)http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Mu_(letter)http://en.wikipedia.org/wiki/Micro-http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Orders_of_magnitude_(numbers)http://en.wikipedia.org/wiki/Milli-http://en.wikipedia.org/wiki/1000_(number)http://en.wikipedia.org/wiki/1000_(number)http://en.wikipedia.org/wiki/Kilo-http://en.wikipedia.org/wiki/1000000_(number)http://en.wikipedia.org/wiki/1000000_(number)http://en.wikipedia.org/wiki/Mega-http://en.wikipedia.org/wiki/1000000000_(number)http://en.wikipedia.org/wiki/1000000000_(number)http://en.wikipedia.org/wiki/Giga-


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Homogeneity and correctness

Note If an equation is homogeneous, itonly means that the equationcould be

correct. For some equations to be correct,

a dimensionless constant is needed.E.g., mv2 gives correct units of energy forkinetic energy (KE) but we need to

get the correct mv2.


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Example2

The thrust, F, on a rocketdepends on the cross-sectional area of the jet, A, the

gas density, , the ejectionvelocity, v. Using dimensional

analysis, find the relationbetween F and other variables.


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Example 3

The volume per second of a liquid flowingthrough a horizontal pipe of length, l, isgiven by the expression:

where kis a dimensionless constant, pisthe excess pressure, ais the radius of thepipe and (/it/ ) is viscosity withdimensions ML-1T-1. Find x.

xkpal


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CHECK LIST

READING: Adams and Allday: Chapter 1 (introductory reading). 2.1, 2.2,2.3, 2.4, 2.5.

At the end of this lecture you should:

Have an understanding of the background and subject matter of physics. Understand what a physical dimensionis and what physical unitsare and

the correspondence between them in the SI system Know what the baseSI units are and what they measure Know the difference between a base unitand a derived unit Be able to define homogeneity Be able to check whether an equation is homogenous Be able to make an educated guess at a physical relationship between

variables, based on whether the equation is homogenous or not.

Saying Greek letters, see:http://en.wikipedia.org/wiki/English_pronunciation_of_Greek_letters

l1 dimensions and scalars

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