Quantity, Symbol, Unit, Unit Symbol

Comments from the Workshop

Revision

Clicking on the link above will take you to the You Must Justify Questions that we didn’t have time for! Please look over this.

Flashcards

CfE Higher Revision Cards A4

Quantity, Symbol, Unit, Unit Symbol

I’ve put together, with Mrs Mac’s help, a document with quantity, symbol, unit and unit symbol so that you know the meaning of the terms in the Relationships Sheet. It is in EXCEL so that you can sort it by course, quantity or symbol.

Quantity, Symbol, Units the excel sheet

Quantity, Symbol, Units a pdf sheet sorted by course and then alphabetical by quantity.

This is the same information in readily available Tablepress form. If you click on the Higher tab at the top it should sort by terms that you need in alphabetical order, or search for a term. Let me know if I’ve missed any.

Quantity, Symbol, Unit, Unit Symbol Table for N5-AH

NHAPhysical Quantity symUnitUnit Abb.
5absorbed dose D gray Gy
5absorbed dose rate H (dot)gray per second gray per hour gray per year Gys-1 Gyh -1 Gyy-1
567acceleration a metre per second per second m s-2
567acceleration due to gravity g metre per second per second m s -2
5activity A becquerel Bq
567amplitude A metre m
567angle θ degree °
567area A square metre m 2
567average speedv (bar)metre per second m s-1
567average velocity v (bar)metre per second m s -1
567change of speed ∆v metre per second m s -1
567change of velocity ∆v metre per second m s-1
5count rate - counts per second (counts per minute) -
567current I ampere A
567displacement s metre m
567distance dmetre, light year m , ly
567distance, depth, height d or h metre m
5effective dose H sievert Sv
567electric charge Q coulomb C
567electric charge Q or q coulomb C
567electric current I ampere A
567energy E joule J
5equivalent dose H sievert Sv
5equivalent dose rate H (dot)sievert per second sievert per hour sievert per year Svs-1 Svh-1 Svy -1
567final velocity v metre per second m s-1
567force F newton N
567force, tension, upthrust, thrustF newton N
567frequency f hertz Hz
567gravitational field strength g newton per kilogram N kg-1
567gravitational potential energy Epjoule J
5half-life t1/2 second (minute, hour, day, year) s
56heat energy Eh joule J
567height, depth h metre m
567initial speed u metre per second m/s
567initial velocity u metre per second m s-1
567kinetic energy Ek joule J
567length l metre m
567mass m kilogram kg
5number of nuclei decayingN - -
567period T second s
567potential difference V volt V
567potential energy Ep joule J
567power P watt W
567pressure P or p pascal Pa
5radiation weighting factor wR- -
567radius r metre m
567resistance R ohm Ω
567specific heat capacity c joule per kilogram per degree Celsius Jkg-1°C -1
56specific latent heat l joule per kilogram Jkg-1
567speed of light in a vacuum c metre per second m s-1
567speed, final speed v metre per second ms -1
567speed, velocity, final velocity v metre per second m s-1
567supply voltage Vsvolt V
567temperature T degree Celsius °C
567temperature T kelvin K
567time t second s
567total resistance Rohm Ω
567voltage V volt V
567voltage, potential difference V volt V
567volume V cubic metre m3
567weight W newton N
567work done W or E Wjoule J
7angle θ radian rad
7angular acceleration aradian per second per second rad s-2
7angular displacement θ radian rad
7angular frequency ω radian per second rad s-1
7angular momentum L kilogram metre squared per second kg m2s -1
7angular velocity,
final angular velocity
ω radian per second rad s-1
7apparent brightnessbWatts per square metreWm-2
7back emfevolt V
67capacitance C farad F
7capacitive reactance Xcohm W
6critical angle θc degree °
density ρ kilogram per cubic metre kg m-3
7displacement s or x or y metre m
efficiency η - -
67electric field strength E newton per coulomb
volts per metre
N C-1
Vm-1
7electrical potential V volt V
67electromotive force (e.m.f) E or ε volt V
6energy level E1 , E2 , etcjoule J
feedback resistance Rfohm Ω
focal length of a lens f metre m
6frequency of source fs hertz Hz
67fringe separation ∆x metre m
67grating to screen distance D metre m
7gravitational potential U or V joule per kilogram J kg-1
half-value thickness T1/2 metre m
67impulse (∆p) newton second
kilogram metre per second
Ns
kgms-1
7induced e.m.f. E or ε volt V
7inductor reactanceXLohm W
7initial angular velocity ω oradian per second rad s-1
input energy E ijoule J
input power Piwatt W
input voltage V1 or V2 volt V
input voltage V ivolt V
6internal resistance r ohm Ω
67irradiance I watt per square metre W m-1
7luminoscityLWattW
7magnetic induction B tesla T
7moment of inertia I kilogram metre squared kg m2
67momentum p kilogram metre per second kg m s-1
6number of photons per second per cross sectional area N - -
number of turns on primary coil np- -
number of turns on secondary coil ns- -
6observed wavelengthλobservedmetrem
output energy Eo joule J
output power Powatt W
output voltage Vo volt V
6peak current Ipeak ampere A
6peak voltage V peak volt V
7phase angle Φ radian rad
67Planck’s constant h joule second Js
7polarising angle
(Brewster’s angle)
ipdegree ̊
power (of a lens) P dioptre D
power gain Pgain - -
7Power per unit areaWatts per square metreWm-2
primary current Ip ampere A
primary voltage Vpvolt V
7radial acceleration ar metre per second per second m s-2
6redshiftz--
67refractive index n - -
6relativistic lengthl'metrem
6relativistic timet'seconds
rest mass mo kilogram kg
6rest wavelengthλrestmetrem
6root mean square current I rmsampere A
6root mean square voltage Vrmsvolt V
7rotational kinetic energy Erotjoule J
7schwarzchild radiusrSchwarzchildmetrem
secondary current Is ampere A
secondary voltage Vsvolt V
7self-inductance L henry H
67slit separation d metre m
7tangential acceleration atmetre per second per second m s-2
6threshold frequency fohertz Hz
7time constanttseconds
7torque Τ newton metre Nm
7uncertainty in Energy∆E jouleJ
7uncertainty in momentum∆px kilogram metre per second kgms-1
7uncertainty in position∆x metre m
7uncertainty in time∆t seconds
6velocity of observer vometre per second m s-1
6velocity of source vsmetre per second m s-1
voltage gain - - -
voltage gain Ao or V gain - -
567wavelengthλmetrem
6work functionWjouleJ

 

2017 Assignment Results

What the 2017 results show is that they final result for the Assignment is mainly down to the way it is written up and not to do with intelligence or choice of topic.

Below is the table of topics covered and scores.

TopicLowest ScoreHighest ScoreNo. of students
Impulse and delta p13172
acceleration due to gravity11163
Exoplanets7132
Fibre Optics12163

Higher Past Papers

I’ve tried to avoid stepping on others toes, but alas, with my big feet I felt I needed to add the Physics Higher Past Papers and Marking Instructions (MI) as well as the PA/Exam/External / Course Reports.

These papers and marking instructions are reproduced to support SQA qualifications, please check the conditions of use and ensure they are not used for commercial benefit.

National Qualification Higher Physics Papers

Digital Paper
(spell)
Higher
Paper
YEARMIExam
Report
NQ H 2019 TEMP SCANNQ 2019 TEMP SCAN H2019Both papers scanned
NH SpecP1
NH Spec P2
SpecMI H P1
MI H P2
NH 20182018MI H 20182018 Report
2017 DQPNH 20172017MI H 20172017 Report
2016 DQPNH 20162016MI H 20162016 Report
2015 DQPNH 20152015MI H 20152015 Report
H S1 DQP
H S2 DQP
NH SpecSpecMI H Spec
Physics
marking
general
principles
READ
THIS!
MARK GUIDE

If you’d like to work through past papers by topic then Mr Davie has done all the hard work for you and has promised to keep this list up to date. He says

This document was created in order to make it easier to find past paper questions both for teachers and students. I will do my best to keep this document up to date and include new past paper questions as they become available. – C Davie Glenrothes High School.

http://bit.ly/HigherPhysics18

Below are the Revised Higher Past Papers, the content is very very similar to the new National (CfE) Higher, although the marks would be different. These were the last past papers with half marks!

Higher
Paper
YEARMIExam Feedback
H Rev 20152015MI Rev 20152015 Report
H Rev 20142014MI Rev 20142014 Report
H Rev 20132013MI Rev 2013
2013 Report
H Rev 20122012MI Rev 20122012 Report
H Rev SpecSpecimen
Paper
MI Rev Spec
READ
THIS
MARK GUIDE

These are the traditional Higher Past Papers (once also known as revised!) Remember some of this material is no longer on the syllabus, and some is relevant to National 5.

Higher
Paper
YEARMarking
Instructions
Exam
Feedback
H 20152015MI 20152015 Report
H 20142014MI 20142014 Report
H 20132013MI 20132013 Report
H 20122012MI 20122012 Report
H 20112011MI 20112011 Report
H 20102010MI 20102010 Report
H 20092009MI 20092009 Report
H 2008 2008MI 20082008 Report
H 20072007MI 20072007 Report
H 20062006MI 20062006 Report
H 20052005MI 20052005 Report
H 20042004MI 20042004 Report
H 20032003MI 20032003 Report
H 20022002MI 20022002 Report
H 20012001MI 2001
H 20002000MI 2000
H Rev Specimen QPSpecimenMI H Rev Specimen

Below is a work in progress of old papers. I am not sure if I’ve overlapped some but I’ll eventually get it all sorted!

Higher
Paper
YEARMarking
Instructions
Exam
Feedback
H 20152015MI 20152015 Report
H 20142014MI 20142014 Report
H 20132013MI 20132013 Report
H 20122012MI 20122012 Report
H 20112011MI 20112011 Report
H 20102010MI 20102010 Report
H 20092009MI 20092009 Report
H 2008 2008MI 20082008 Report
H 20072007MI 20072007 Report
H 20062006MI 20062006 Report
H 20052005MI 20052005 Report
H 20042004MI 20042004 Report
H 20032003MI 20032003 Report
H 20022002MI 20022002 Report
H 20012001MI 2001
H 20002000MI 2000

From National Parent Forum of Scotland This great little pdf file gives some ideas of suitable questions from the traditional Higher papers that are suitable for the new National Qualifications.

Thanks to Mr John Irvine for filling in most of the gaps in the Exam Reports, and to Mr Stuart Farmer for making it a full house, only a few left to fill. PLEASE can I recommend that both teachers and students READ the Report after tackling the past paper. The course reports give really good background and information about how candidates performed in the exam and what messages you should learn from them. Believe it or not, candidates often make the same mistakes every year! The reports are designed to help you learn from this.

Please also note that some of the National Higher content was once in the AH course, so it is worth checking these papers for some additional practice.

The papers pre-2000 can be found at http://mrmackenzie.co.uk/higher-revision/

I’ve added some info in here until Mr Mackenzie’s fab site is back up. Thanks to Mr Mallon, the originator of online resources!

Higher
Paper
YEARMarking
Instructions
1999H 1999 PI Solutions
H 1999 PII Solutions
1998H 1998 PI Solutions
H 1998 PII Solutions
1997H 1997 PI Solutions
H 1997 PII Solutions
1996H 1996 P1 Solutions
H 1996 PII solutions
1995H 1995 PI Solutions
H 1995 PII Solutions
1994H 1994 PI Solutions
H 1994 PII Solutions
1993H 1993 PI Solutions
H 1993 PII Solutions
1992H 1992 PI solutions
H 1992 PII Solutions
1991

All the best with your revision!

Signature

Uncertainties

It is really important that you get to grips with the uncertainty section. You will need this information for your Assignment and it could well form a question on the exam paper.

The key is remembering that ANY measurement is liable to uncertainty. Get that and you’re half way there!

CONTENT ASSOCIATED WITH UNCERTAINTIES

Random and systematic uncertainty

Uncertainties and data analysis

  • All measurements of physical quantities are liable to uncertainty, which should be expressed in absolute or percentage form. Random uncertainties occur when an experiment is repeated and slight variations occur. Scale reading uncertainty is a measure of how well an instrument scale can be read. Random uncertainties can be reduced by taking repeated measurements.Systematic uncertainties occur when readings taken are either all too small or all too large. They can arise due to measurement techniques or experimental design.
  • The mean of a set of readings is the best estimate of a ‘true’ value of the quantity being measured. When systematic uncertainties are present, the mean value of measurements will be offset. When mean values are used, the approximate random uncertainty should be calculated. When an experiment is being undertaken and more than one physical quantity is measured, the quantity with the largest percentage uncertainty should be identified and this may often be used as a good estimate of the percentage uncertainty in the final numerical result of an experiment. The numerical result of an experiment should be expressed in the form final value ±uncertainty.

UNCERTAINTIES NOTES

Whenever you do an experiment there will be uncertainties.

There are three types of uncertainty and effects to look out for at Higher.

Systematic Effects

Here the problem lies with the design of the experiment or apparatus. It includes zero errors. Sometimes they show up when you plot a graph but they are not easy to recognise, as they are not deliberate. Systematic effects include slow running clocks, zero errors, warped metre sticks etc. The best way to ensure that these are spotted is to acknowledge their existence and go looking for them. Where accuracy is of the utmost importance, the apparatus would be calibrated against a known standard. Note that a systematic effect might also be present if the experimenter is making the same mistake each time in taking a reading.

Random Uncertainties

These uncertainties cannot be eliminated. They cannot be pinpointed. examples include fluctuating temperatures, pressure and friction. Their effect can be reduced by taking several readings and finding a mean.

Reading Uncertainties

These occur because we cannot be absolutely certain about our readings when taking measurements from scales. Use scales with mirrors where possible, good scales and repeat all measurements.

Repeat all experiments to reduce the reading and random uncertainties. Systematic effects are not improved by taking lots of results.

Which experiment has the best design?

Quantifying Uncertainties

 1.Find the mean

This is the best estimate of the “true” value but not necessary the “true” value.

          2. Find the approximate random uncertainty in the mean (absolute uncertainty)

This can be written as  and it is sometimes referred to as average deviation or absolute uncertainty.

3. Find the percentage uncertainty.

or

Scale Reading Uncertainty

This value indicates how well an instrument scale can be read.

An estimate of reading uncertainty for an analogue scale is generally taken as:

± half the least division of the scale.

Note: for widely spaced scales, this can be a little pessimistic and a reasonable estimate should be made.

For a digital scale it is taken as

± 1 in the least significant digit displayed.

Or uncertainty in reading ÷reading × 100%

Overall final Uncertainty

When comparing uncertainties, it is important to take the percentage in each.

In an experiment, where more than one physical quantity has been measured, spot the quantity with the largest percentage uncertainty. This percentage uncertainty is often a good estimate of the percentage uncertainty in the final numerical result of the experiment.

eg if one measurement has an uncertainty of 3% and another has an uncertainty of 5%, then the overall percentage uncertainty in this experiment should be taken as 5%

 

Signature


Introduction Tasks

Friday 9th June
learning outcomes
  1. To review the work completed so far
  2. To practice uncerts and practical experiments
  3. To practice risk assessments

    tasks

    1. Starting on approximately p14 of the introduction notes complete tutorial 1 & 2
    2. Make notes on uncerts and quantifying them from chapter 4
    3. Risk assessment -Go through the powerpoint on the network (higher physics-> intro-> on risk assessment)
    4. In your classwork jotter answer the questions as you go through the power point
    5. Complete the practical below and write it up, including hazards, risks and controls.
    Checking Your Uncertainties.

    Aim:      To find the average speed of a trolley moving down a slope, estimating the uncertainty in the final value.

    Apparatus: 1 ramp, 1 metre stick, 1 trolley, 1 stop clock.

    Instructions:

    1. Set up a slope and mark two points 85 cm apart.
    2. Note the scale reading uncertainty.
    3. Calculate the percentage uncertainty in the distance.
    4. Ensuring the trolley starts from the same point each time, measure how long it takes the trolley to pass between the two points.
    5. Repeat 5 times, calculate the mean time and estimate the random uncertainty.
    6. Note the scale reading uncertainty in the time.
    7. Calculate the percentage uncertainty in the time.
    8. Calculate the average speed and associated uncertainty.
    9. Express your result in the form:

    (speed ± absolute uncertainty) m s-1

    Write up your experiment and include your risk assessment

    1. Continue with the tutorials on Uncerts.

Outcome 1

Before you can pass any units you must have completed an Outcome 1. This is a practical activity that you must have been involved in. You should have collected data and written it up. See the instructions below.

There is also included below a front marking sheet that you ought to place on the front of your submitted write up.

O1 mark sheet

O1 mark sheet

CANDIDATE GUIDE

Your plan must include:
• an aim — which is a clear statement of what you are trying to do in this experiment/practical investigation
• the dependent and independent variables
• the relevant variable(s) to be kept constant
• what you will be measuring/observing
• a list of equipment/materials you will use
• a labelled diagram of the experimental arrangement, if appropriate
• a description of how you will carry out your experiment/practical investigation (including safety where appropriate)
Checkpoint: Ask your assessor to check your plan before you start the practical work.
• You should carry out your experiment/practical investigation safely, including repeated measurements and averages where appropriate.
• Record your observations/measurements in an appropriate way.
Checkpoint: Ask your assessor to check your results.
• Present your findings/results in any appropriate format. You should:
— record the information/data in a clear and systematic way, with well-organised tables of raw data
— process/analyse the results. Present your findings in any appropriate format. These may be from: a table, line graph or summary. Graphs should be plotted on squared graph paper
— use appropriate SI units and standard abbreviations
• State your conclusion(s) — which should reference the aim.
• Evaluate your experimental procedures, with justification(s). Your evaluation should include two possible improvements and be supported by justification(s).

Outcome 1

1 Apply skills of scientific inquiry and draw on knowledge and understanding of the key areas of this Unit to carry out an experiment/practical investigation by:
1.1 Planning an experiment/practical investigation
1.2 Following procedures safely
1.3 Making and recording observations/measurements correctly
1.4 Presenting results in an appropriate format
1.5 Drawing valid conclusions
1.6 Evaluating experimental procedures

To pass this assessment you will have to show that you have met this Outcome and Assessment Standards.
Your assessor will let you know how the assessment will be carried out and any required conditions for doing it.

What you have to do
This assessment activity is an experiment/practical investigation.
Your assessor will provide you with the resources you need. You may be able to work in a group to do the practical work, but your assessor will need you to show that you have met the Assessment Standards.
To pass this assessment, you will have to prepare a scientific report to show that you can:
• plan an experiment/practical investigation
• make and record observations/measurements correctly
• present your results in an appropriate format
• draw valid conclusions
• evaluate experimental procedures
While you are carrying out your experiment/practical investigation, your assessor will be observing to make sure that you are following procedures safely, and that you are making measurements correctly.

Experimental Write Up

Your best work. Rulers, sharp pencils, colour etc.

Correct use of terminology and units at all times

NO WAFFLE!

Title   Short and relevant with date.

Aim     What are you trying to find out/prove?

To find out how “something” affects “something else”.

 

Method     Instructions on how to complete the experiment; make it reliable and make it a fair test:

Set up the following apparatus (draw a good labelled diagram).

The “something” was set at a “value” and increased by an “amount” using the “piece of equipment”.  The “something else” was noted    at each value using the “other piece of equipment”.  Other variables were kept constant by…….

Results     Display the findings.

A neat table with headings and units.

An appropriate graph of somethingon the x-axis andsomething elseon the y-axis.

Conclusion    What did you find out?

As the “something” is increased / decreased, the “something else” increased / decreased / stayed the same.  Also include “directly/inversely proportional” if appropriate.

Evaluation    Are there any improvements that could be made to your experiment to reduce uncertainties?

 

Signature


 

Special Relativity & Web-based Research

Communicating Scientific Results

Here is a chance for you to practice some of the skills required for your Investigation. This task gives you some practice to help with your Researching Physics topic. It is to help you look at ways of communicating and think who you are communicating to.Log all the work that you do for this section in your Researching Physics Log Book.

Objective

You will look at the various ways in which findings can be presented, and appreciate the possibility of using other media such as video clips, articles, papers, posters etc.

Learning outcome

You will be more informed about the different ways in which one topic can be presented. You will begin to think about how to present your own work.

Learning activity

You can work independently or in groups. There are three different resources:

  1. A video clip entitled ‘Two postulates’ (http://www.youtube.com/watch?v=WdfnRWGgbd0).

    If you can’t read the file above it has been uploaded here as an MP4 file.

  2. A physicsworld article entitled ‘Slowed Light Breaks Record’

PHYSICS WORLD ARTICLE DECEMBER 2009

3. The paper

‘On Velocities Beyond the Speed of Light c’ (On Velocities beyond the speed of light c.pdf) On Velocities beyond the Speed of Light

You should examine and discuss the three resources. Teachers should point out that even though the physics content may not all be at the students’ level of understanding, it is still possible to take information from it with their level of knowledge. This is emphasised by you completing the work below.

‘Two Postulates’

This clip discusses how to tell if an object is moving or not by way of an animation.

‘Slowed Light Breaks Record’

This is an article published in physicsworld in December 2009. It is not particularly long, although does contain a lot of information.

‘On Velocities Beyond the Speed of Light c’

This paper was published in 1998 from CERN. It has the more traditional scientific report structure and is a good example for you.

After completing the table on the sheet, you should find that all boxes are ticked – highlighting that even though the information is presented in different ways, all the resources contain what the students will have to put into their own reports.

There are many ways to present scientific findings. You might have written a report in the past but universities may ask you to present a poster of your work.

Here we will look at three different ways of presenting findings on special relativity.

On your own or in groups/pairs, have a look at the three examples of how findings on special relativity have been presented.

Copy and complete the table, either with a few notes or a tick or cross, to show if the example meets the criteria.

‘Two Postulates’ ‘Slowed Light Breaks Record’ ‘On Velocities Beyond the Speed of Light’
Is there mention of the objective for the investigation/experiment?
Is there information given on the experiment/s conducted?
Is there mention of the data (perhaps not all) and any analysis of the findings?
Does the article discuss the conclusion for the experiment/investigation?

Now you have looked at the three examples, ask yourself the following questions.

First impressions
  1. Was one resource more eye-catching than the others?
  2. Does one look like it will be easier to read/understand than the others?
  3. Which one looks most credible?
Down to the nitty gritty
  1. Which resource was the most interesting?
  2. Which one was the best presented?
  3. Which gave the most information?
  4. Did you need to understand everything mentioned to gain an understanding of the experiment?

Which format might you consider for your Communicating Physics investigation?

More information on Web-Based Research

Web-Based Research HApr16 A powerpoint presentation showing how to help you find viable websites

Web-Based Research Student Materials Some materials to give you advice on using websites.

Physics Web-Based Research Worksheets Material that you can work through to give you practice at completing web-based tasks.

 

Signature


Measurement of acceleration due to gravity

Below are some links and documents for the Researching Physics dealing with measurement of the acceleration due to gravity.

http://practicalphysics.org/measurement-g-using-electronic-timer.html

http://www.practicalphysics.org/acceleration-due-gravity.html

 

 

 

 

 

 

 

 

 

https://revisionworld.com/a2-level-level-revision/physics/fields-0/gravitational-fields-0

The information below is based on the material found from the website above. TBC!

Fields

A field is a region of space where forces are exerted on objects with certain properties. Three types of field are considered:

  • gravitational fields affect anything that has mass
  • electric fields affect anything that has charge
  • magnetic fields affect permanent magnets and electric currents.

These three types of field have many similar properties and some important differences. There are key definitions and concepts that are common to all three types of field.

Gravitational fields

Newton realised that all objects with mass attract each other. This seems surprising, since any two objects placed close together on a desktop do not immediately move together according to Newton’s second law F=ma. The attractive force between them is tiny, and very much smaller than the frictional forces that oppose their motion.

Gravitational attractive forces between two objects only affect their motion when at least one of the objects is very massive. This explains why we are aware of the force that attracts us and other objects towards the Earth – the Earth is very massive. The mass of the Earth is about 6 × 1024 kg.

The diagram represents the Earth’s gravitational field.

The lines show the direction of the force that acts on a mass that is within the field.

This diagram shows that:

  • gravitational forces are always attractive – the Earth cannot repel any objects
  • the Earth’s gravitational pull acts towards the centre of the Earth
  • the Earth’s gravitational field is radial; the field lines become less concentrated with increasing distance from the Earth.

The force exerted on an object in a gravitational field depends on its position. The less concentrated the field lines, the smaller the force. If the gravitational field strength at any point is known, then the size of the force can be calculated.

The gravitational field strength, g, at any point in a gravitational field is the force per unit mass at that point

g=F/m

Close to the Earth g has the value of 9.8 Nkg-1

Gravitational field strength is a vector quantity, its direction is towards the object that causes the field.

Universal gravitation

Newton concluded, during his work, that the gravitational attractive force that exists between any two masses:

  • is proportional to each of the masses
  • is inversely proportional to the square of their distances apart.

Newton’s law of gravitation describes the gravitational force between two points. It can be written as

F=(GMm)/r2

Where

G is the universal gravitational constant and is equal to 6.67 × 10-11 N m2 kg-2  .   M and m are the magnitude of the masses and r is the separation between  the centre of the masses.

A point mass is one that has a radial field, like the Earth as shown in the diagram above.

Although the Earth is a large object, on the scale of the Universe it can be considered to be a point mass. The gravitational field strength at its centre is zero, since attractive forces pull equally in all directions. Beyond the surface of the Earth, the gravitational force on an object decreases with increasing distance. When the distance is measured from the centre of the Earth, the size of the force follows an inverse square law; doubling the distance from the centre of the Earth decreases the force to one quarter of the original value.  The two objects attract each other with equal sized forces and act in opposite directions. The variation of g with distance from the surface of the Earth is shown in the diagram.

g and G 

Newton’s law of gravitation can be used to work out the value of the force between any two objects. It can also be used to calculate the strength of the gravitational field due to a spherical mass such as the Earth or the Sun.

F=(GMm)/r2

As the value of F is also the weight then we can equate these two quantities, so that g not only equals W/m but also g=(GM)/r2 as below

Gravitational field strength is a property of any point in a field. It can be given a value whether or not a mass is placed at that point. Like gravitational force, beyond the surface of the Earth the value of g follows an inverse square law.

Because the inverse square law applies to values of g when the distance is measured from the centre of the Earth, there is little change in its value close to the Earth’s surface. Even when flying in an aircraft at a height of 10 000 m, the change in distance from the centre of the Earth is minimal, so there is no noticeable change in g. The radius of the Earth is about 6.4 × 106 m, so you would have to go much higher than aircraft-flying height for g to change by 1%.

The same symbol g is used to represent:

  • gravitational field strength
  • free-fall acceleration.

These are not two separate quantities, but two different names for the same quantity. Gravitational field strength, g, is defined as the force per unit mass, g = F/m.

From Newton’s second law and the definition of the newton, free-fall acceleration, g, is also equal to the gravitational force per unit mass. The units of gravitational field strength, N kg–1, and free-fall acceleration, m s–2, are also equivalent.