1. Physics and Physical Measurements

2. Nature provides different experiences to the mankind.
These experiences are scientifically termed as Physical quantities
we have two types of physical quantities.
Fundamental quantities
Derived quantities

3. Fundamental Derived These are independent Eg: Mass, Length, Time ,….
They have fundamental units like kg  mass m  Length S  Time
These are dependent on Fundamental
Eg: area, volume, density, force,….
They have derived units like m2  area m3  Volume kg/m3  Density

4. Order of magnitude This is power of 10
It is helpful to avoid getting lost among the numbers
Eg. The diameter of an atom, 10-10m does not sound much larger than diameter of proton in its nucleus, 10-15m.
But the ratio between them is 105 or times bigger. This is we say a difference of 5 orders of magnitude’
Atom is football pitch and nucleus is a pea on the centre circle.
Site add: to see macro to micro
Site add: to see quarks to outer space

5. Range of masses
1052
10-31
10-8 Kg
Mass of the
Observed
universe
Mass of
Milky way galaxy
electron
Grain of sand/
Blood corpuscle
Mass of
the earth
Most fundamental particle is quark and it hides inside proton and neutron.
the lightest quark is up quark , whose mass is about kg.

6. Range of lengths
1026
10-15
10-10 m
Radius of
Observed universe
Distance of
Earth to sun
Diameter
of proton
Diameter
of atom
Radius of
the earth
There is a much smaller fundamental unit of length, Planck length,
which is around m.

7. Range of Time
100 s
10-8
Heart beat
Age of the earth
Age of the universe
Passage of
Light across
A nucleus
Passage of
Light across
An atom
Passage of
Light across
A room
What is theoretical lower limit of time?
Estimation – what is ratio of rest mass of proton to rest mass of electron?
Theoretical lower limit of time = s/v = 10-35/108 = s - TOK discussion

8. Significant figures
These are number of digits up to which we are sure about their accuracy.
Significant figures do not change if we measure a physical quantity in different units.
E.g cm = m = 14.5 X 10-2 m
Here three values have same
significant figures i.e. 3

9. Rules for significant figures
All non zero digits are significant figures.
17 - 2
All zeros occurring between non zero digits are significant figures.
All zeros to the right of the last non zero digit are not significant figures.
20 - 1

10. All zeros to the right of a decimal point and to the left of a non zero digit are not significant figures.
All zeros to the right of a decimal point and to the right of a non zero digit are significant figures.

11. Exercise on significant figures
State the number of significant figures in the following:
0.005 m2
2.63 X 1028 kg
g. cm-3
6.320 N
200.05

12. Fundamental units unit Symbol Quantity kilo gram Kg Mass Metre M
Length
second S
Time
ampere A
Current
kelvin K
Temperature
Mole
mol
Amount of matter
candela Cd
Intensity of light

13. Derived units Quantity Formula Unit Area l x l m2 Volume l x l xl m3
Density
Mass/volume
kg.m-3
Velocity
Distance/time
m.s-1
Acceleration
Velocity/time
m.s-2
Force
Mass Xacceleration
kg.m.s-2 (N)
Work/energy
Force Xdisplacement
Kg.m2.s-2 (J)
For other derived quantities refer course companion

14. Conversion between units
CGS system VS SI system
1m = 100 cm, 1kg = 1000 g, 1min = 60 s, 1h = 60 min = 3600 s
1kmph = _______ m.s-1
Kg.m.s-2 = __________ g .cm .s-2
Kg.m2.s-2 = __________ g.cm2.s-2
1 kwh = ___________ J
1 eV = _____________ J

15. SI Prefixes Prefix Symbol Value tera T 1012 giga G 109 mega M 106 kilo
103
centi c
10-2
milli m
10-3
micro μ
10-6
nano n
10-9
pico p
10-12
femto f
10-15

16. Exercise on prefixes Change 236000 J to MJ
Radio frequency is Hz. Change in GHz
Wavelength of white light is 5.0 x 10-7m. Express in nanometre.
Time of an event is 1 x 10-6s. Express in prefix format.
Change 1 M W to K W
Change 1nm into 1pm

17. Significant figures in algebric operations
Addition and subtraction operation
When we add two like quantities, then the final result cannot be more accurate than the least precise quantity.
E.g. sum of 2.3 m and m = m, but 2.3 m is the least precise. i.e. it is accurate up to 0.1 m . Hence the final result will be 12.8 m.
Multiplication and division operation
When we multiply two quantities, then the final result cannot be more accurate than the least precise quantity.
e.g. product of and 2.02 = , but 2.02 is the least precise. Hence the final result will be 8.47

18. Accuracy & Precision
Accuracy tells how close the measured value is to the true value of the quantity.
Precision tells us to what resolution or limit the quantity is measured.
E.g. suppose the true value of a certain length is cm. in one exp, using instrument of precision 0.1 cm, the measured value found to be 4.7 cm, while in another exp using instrument of precision 0.01 cm, the length found to be 4.56 cm.
Here first measurement has more accurate but less precision.
Second measurement has more precision but less accurate.

19. Bull’s eye game Precise, not accurate Accurate, not precise
Neither precise nor accurate
Both accurate and precise

20. Uncertainty or error in measurement
The difference in the true value and measured value is called error.
Types of error
Random error
Systematic error
usually random errors are caused by the person doing the experiment.
Causes –
changes in the experimental conditions like temp, pressure or humidity etc..
A different person reading the instrument
Malfunction of a piece of apparatus

21. Systematic error
This error is due to the system or apparatus being used.
Causes –
An observer consistently making the same mistake
An instrument with zero error
Apparatus calibrated incorrectly
How to avoid the errors?
Random errors can be reduced by repeating the measurement many times and taking the average, but this process will not effect systematic errors.
An accurate experiment is one that has a small systematic error, where as a precise experiment is one that has a small random error.

22. Measuring tools Metre scale Vernier calipers Screw gauge Beam balance
Common balance
Spring balance
Stop watch

23. Mathematical representation
of uncertainties
Absolute error (Absolute uncertainty) – It is the magnitude of difference between true value of quantity and the measurement value. If p is the measured quantity then absolute error expressed as ±∆p
Relative error (Fractional uncertainty)– The ratio of absolute error to the true value of the physical quantity is called relative error. Here ±∆p is the relative error P
Percentage error (Percentage Uncertainty) – relative error X 100% = ±∆p X 100% P

24. Example:
mass of a body is (20 ± 0.2) Kg. Here
absolute uncertainty = ± 0.2 kg relative uncertainty = 0.2 = ± 0.01 20
Percentage uncertainty = 0.01 X 100% = 1%
So mass of a body = 20Kg ± or 20 kg ± 1%

25. Uncertainty in Addition and Subtraction A, B are two quantities and Z = A + B or Z = A - B ∆A, ∆B, ∆Z are uncertainties in A, B, Z respectively then ∆Z = ∆A + ∆B
Uncertainty in Multiplication and Division A, B are two quantities and Z = A X B or Z = A / B ∆A, ∆B, ∆Z are uncertainties in A, B, Z respectively then ∆Z = ∆A + ∆B Z A B
Uncertainty in powers A is quantity and Z = An then ∆Z = n ∆A Z A

26. Numericals
Two bodies have masses (20 ± 0.2) Kg and (30 ± 0.4) Kg. what is the total mass of these bodies?
Area of a rectangle field is A = l X b , l = (200 ± 5) m and b = (50 ± 2) m. find the percentage error in A?
Density of a substance is d = m/v , m = (20 ± 0.2) Kg and v= (10 ± 0.1) m3. Calculate the percentage error of d?
A physical quantity Z is given by Z = a2b3 . Calculate the relative c4 and percentage error in Z.
the percentage errors in the measurement of mass and speed are 2%, 3% respectively. How much will be the max error in the estimate of the KE?

27. Graphs introduction The graph should have a title.
The scales of the axes should be suitable – there should not be any sudden or uneven jumps in the numbers.
The inclusion of the origin has been thought about. You can always draw a second graph without it if necessary.
The final graph should cover more than half the paper in either direction.
The axes are labelled with both the quantity and units
The points are clear. Vertical and horizontal lines to make crosses are better than 45 degrees crosses or dots.

28. All the points have been plotted correctly.
Error bars are included if necessary.
A best fit line is added. It is there to show overall trend.
If best fit line is a curve, this has been drawn as a single smooth line.
As a general rule, there should be roughly the same number of points above the line as below the line.
Any points that do not agree with the best fit line have been identified.

29. Gradient and intercept
A straight line graph can only intercept (cut) either axis once and often it is y – intercept.
if a graph has an intercept of zero it goes through the origin. (proportional)
y intercept

30. Gradient or slope
It is the ratio of change in y – axis to the change in x – axis.
i.e. m = ∆y ∆x
A straight line graph has a constant gradient.
The triangle used to calculate the gradient should be as large as possible.
The gradient has units.
The gradient of a curve at any particular point is gradient of the tangent to the curve at that point. ∆y ∆x ∆y ∆x

31. Area under a graph
it is the product of quantity on y axis and by the quantity on x axis.
i.e. Area = quantity on y X quantity on x
If the graph is a curve, the area can be calculated by counting the squares and working out what one square represents.
The units for the area under graph are the units on the y axis multiplied by the units on the x axis.

32. Exercise what is the slope of distance – time graph?
What is the slope, area of speed – time graph?
What is the area of acceleration – time graph?
If v = at + u represents y = mx + c then find m, y intercept and show them in a rough graph?

33. Exercise on graphs
The following data is about to find acceleration due to gravity using simple pendulum.
draw a graph between l (y – axis), t2 (x – axis) show that it is a st line.
Find the slope of the graph and find the g using the formula g = 4π2.l/t2
l cm
T2 (s) 50
1.96 60
2.37 70
2.77 80
3.18 90
3.50
100
3.92
110
4.35
120
4.74

34. The following data is about to show that n2 (v+e) = const, where n = frequency of tuning fork, v = volume of the air in the volume resonating column, e = end correction in volume resonance exp
n(Hz)
V (ml)
384
294
320
437
256
652
512
172
Draw a graph between 1/n2 (X – axis), v (Y – axis) and show that it is a st line.
Find slope and y intercept and label it as e.
Compare the above eq with y = mx +c and write the slope and y intercept.

35. Uncertainties in graphs
Uncertainties in graphs can be shown as error bars
Uncertainties are many types.
With analog instruments, such as rulers, you would add onto the end of a value a plus or minus half the value of the last digit, eg. on a ruler with 1mm precision, you would put +/- .5mm.
Digital instruments use a different system, where it is plus or minus the value of the last digit, eg. with an electronic scale that reads 291g, the uncertainty would be +/- 1g.
We take a time of 8.06 s with a stopwatch that measures 1/100 seconds, so half the limit of reading would be s. But we know from experience that our reaction time is longer than that, so we estimate it to for example 0.10 s, and have the result 8.060.1s.

36. If we have several (at least about 5) measurements of the same thing, we can use the highest residual as an absolute uncertainty. A residual = the absolute value of the difference between a reading and the average of the readings.
Ex. Five people measure the mass of an object. The results are 0.56 g, 0.58 g, 0.58 g, 0.55 g, 0.59g.
The average is (0.56g g g g g)/5 = 0.572g
The residuals are 0.56g g = (-) 0.012g, 0.58g g = 0.008g, 0.58g g = 0.008g, 0.55g g = (-)0.022 g, 0.59g g = 0.018g
Then the measurement is m = 0.572g0.022g or sometimes 0.570.02g (uncertainties are usually approximated to one significant digit).

37. To change curve in to linear line Click on the measurements
To know how to draw max , min gradients click on maxmin gradient
Make the students to draw graph with error bars manually and electronically (Excel)

38. Vectors
Vector – which having magnitude and direction e.g. displacement, velocity, acceleration, force, momentum, impulse, torque,….etc
Scalar – which having only magnitude e.g. distance, speed, time, mass, temp, current, charge, potential,…etc.
Vector Representation p o A
Magnitude = |p|
Direction = towards east
Vector = OA or p

39. Concepts to be discussed
Vector addition
Polygon law
Vector subtraction
Exercise
Vector resolution – importance
Examples on resolution
Force and displacement
Inclined plane
Rain fall
Exercise from text book/ reference book