This lecture overview covers several topics in physics including space and time, units and dimensions, kinematics, statics and dynamics, moments and rotation, elasticity, hydrostatics, temperature, sound waves, and wave properties. The key concepts that will be discussed include physical quantities, units, and dimensional analysis. Dimensional analysis is used to determine the relationships between different physical quantities and check the consistency of equations. The lecture also introduces various motion concepts like displacement, velocity, acceleration, and force as well as other physics principles.

1. Lecture Overview
1. Space and time; physical quantities, units, dimension and dimensional
analysis
2. Kinematics; Fundamental laws of mechanics,
3. Statics and dynamics; work and energy. Conservation laws.
4. Moments and energy of rotation; simple harmonic motion; motion of
simple systems;
5. Elasticity; Hooke's law, Young's shear and bulk moduli,
6. Hydrostatics; Pressure, buoyancy,Archimedes' principles.
7. Surface tension; adhesion, cohesion, capillarity, drops and bubbles.
8. Temperature; heat, gas laws; Laws of thermodynamics; kinetic theory of
gases.
9. Sound; Types and properties of waves as applied to sound and light
energies.
10. Superposition of waves. Propagation of sound in gases, solids and liquids
and their properties.
11. The unified spectra analysis of waves. Applications.

2. SP
ACEAND TIME; UNITSAND DIMENSION.
LECTURE 1

3. Contents of Chapter 1
• The Nature of Science
• Physics and Its Relation to Other Fields
• Models, Theories, and Laws
• Measurement and Uncertainty; Significant Figures
• Units, Standards, and the SI System
• Converting Units
• Order of Magnitude: Rapid Estimating
• Dimensions and DimensionalAnalysis
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4. Introduction
• Physics as a branch of science, deals with nature
and the relationship between matter and energy.
• It is the natural science that is based on
experiments, measurements and mathematical
analysis with the purpose of finding physical
laws that govern everything in the universe.
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5. Nature of Science
The process involved before a law in physics is
accepted:
• Hypothesis
• Theories
• Law
• Model
• Principles
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6. Hypothesis:
• A tentative explanation that can be tested by
further investigation.
• Experiment is a controlled method of testing a
hypothesis
• Example: Avogadro's hypothesis
Nature of Science

7. Theory
• A comprehensive explanation of an important feature of
nature supported by facts that have been repeatedly
confirmed through observation and experimentation over
time.
• Quantitative description of experimental observations.
Not just WHAT is observed but WHY it is observed as it
is and HOW it works the way it does.
• Example: Brownian theory
• Tests of theories:
– Experimental observation:
More experiments, more observation.
– Predictions:
Made before observations & experiments.
Nature of Science

8. Law:
• they are similar to scientific theories in that they
are principles that can be used to predict the
behavior of natural world. Both law and theories
are well supported by observation and/or
experimental evidence.
• It summarizes the relationship between variables.
E.g Newton’s law.
• The difference between them are:
• Law are frequently written as an equation and
describes what happens.
• Theories are more of explanation. It explains why
we observe what we do.
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Nature of Science

9. Model:
• Models are very useful during the process of
understanding phenomena. An analogy of a physical
phenomenon to something we are familiar with.
• A model creates mental pictures; care must be taken to
understand the limits of the model and not take it too
seriously.
• A description, simulation, graphic, or 3-D representation
of theory used to help enhance understanding.
Example:
• The Bohr model of the atom, for example, depicts
electrons circling the atomic nucleus in a fashion similar
to planets in the solar system, but it is by no means
represents the true nature of the atom.
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Nature of Science

10. Principles:
Principles are approaches to analyzing a problem
and serve as templates for setting up equations
specific to your problem.
Aprinciple is similar to a law, but applies to a
narrower range of phenomena.
Example:Archimedes Principles
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Nature of Science

11. Physical Quantities
• Physical quantities are physical properties in
physics that can be measured.
• They have two parts: eg. 20 kg
• 1. Numerical
• 2. Alphabetical
• Numerical part : size/magnitude
• Alphabetical part: it is the quantity that
specifies the specific physical quantity-SI unit.
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12. Unit
Definition:
• A unit is a physical quantity that can be counted or
measured using standard size defined by custom
or law.
• unit as used in physics refers to the standard measure of
a quantity.
• Every measurement or quantitative statement requires a
unit.
• Example: 20 sugar does not mean anything, rather 20 kg
of sugar.
There are two categories of units
1. fundamental/base units
2. Derives units
Physical Quantities

13. Units
• If a unit becomes officially accepted, it is
called Standard Unit.
• Group of Unit and Combination is called
SYSTEM OF UNITS.
Example: SI Units, British Units
SI = International Systems of Units
Physical Quantities

14. UNIT SYSTEMS
Full forms of different standard systems:
1.The full form of CGS system is Centimeter Gram Second system.
In the CGS system, fundamental units are Centimeter, Gram, and
second
2.The full form of FPS system is Foot Pound Second system. In the
FPS system, fundamental units are Foot, Pound, and second.
3.The full form of MKS system is Meter Kilogram Second system.
In the MKS system, fundamental units are meter, kilogram, and
second.
4.The full form of SI is System International(International System
of Units). In the SI system, the fundamental units are Meter,
Kilogram, and Second.

15. • All things in classical mechanics
can be expressed in terms of base
quantities:
• Length (L),MASS(M), TIME (T)
❑ British Units:
L= inches, feet,
miles,
M = slugs (pounds),
T = seconds
MKS system CGS System
L = meters (m) centimeter (cm)
M = kilograms (kg) gram (g)
T = seconds (s) seconds (s)
Physical Quantities
Units
• SI (Système International) Units also
called Metric System

16. Units, Standards, and the SI System
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Quantity Unit Standard
Length Meter Length of the path traveled by
light in 1/299,792,458 second.
Time Second Time required for 9,192,631,770
periods of radiation emitted by
cesium atoms
Mass Kilogram Platinum cylinder in
International Bureau of Weights
and Measures, Paris

17. Units, Standards, and the SI System
These are the standard
SI prefixes for
indicating powers of 10.
Many are familiar; Y
, Z,
E, h, da, a, z, and y are
rarely used.
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18. Converting Units
Converting between metric units, for example from
kg to g, is easy, as all it involves is powers of 10.
Converting to and from British units is considerably
more work.
For example, given that
1 m = 3.28084 ft, this
8611-m mountain is
28251 feet high.
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19. Unit Conversion

20. The advantages of S.I. system
(i) S.I. has broader base. It has seven base units and two
supplementary units.
(ii) S.I. is rational, i.e., This system makes use of only one unit for one
physical quantity, e.g., for energy of any type, i.e., mechanical or
heat or electrical. There is only one unit, Joule (J) but in M.K.S.
system unit for mechanical energy is Joule.
(iii) S.I. is coherent. In this system, all the derived units can be easily
obtained from basic and supplementary units
(iv) S.I. is metric system which means that multiples and submultiples
can be expressed as powers of 10.
(v) S.I. is the modernised and improved form of M.K.S. system so it
is readily accepted in almost all the countries of the world.
(vi) The symbols fixed by S.I. are not subject to change whatever may
be the language, e.g., unit of mass kilogram having symbol ‘kg’
has to be written like this only in French or German or Hindi or
Punjabi etc.

21. Disadvantage of SI Unit
It has disadvantages such as it mainly focuses on
only one unit so the importance of other units is
diluted.
Also the SI unit cannot always accurately define a
quantity.

22. Physical Quantities
Categories of physical quantities:
1. Fundamental/base
2. Derived
3. Supplementary
• Fundamental/base
• They are quantities which are distinct in nature
that cannot be defined by other quantities but
upon which other physical quantities are
derived.
• There are 7 base quantities
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23. Fundamental/base quantities
• Definitions:
• Mass - is the amount of substance or material in an object.
• Length - is the distance between two points.
• Time - is the duration between two instants or events.
• Current - is the flow of electrons from a high potential to a low
potential.
• Temperature - is the measure of how hot or cold an object or
substance is based on a comparative scale.
• Amount of Substance - is a measure of the amount of
elementary entities such as atoms, molecules and other
particles.
• Luminous Intensity - is a measure of the amount of light that a
point source radiates in a given direction.

24. Physical Quantities
• Fundamental/base quantities

25. Derive quantities
• They are quantities whose definitions are based
on other physical quantities (fundamental
quantities) by multiplication or division or both.
• A derived quantity is produced when two (2) or
more fundamental quantities are combined, either
by multiplication or division.
Physical Quantities

26. Derive quantities
• Definitions:
• Displacement - is how far off an object is from its rest position, usually a
straight line distance.
• Speed - is how fast an object is moving.
• Velocity - is how fast an object is moving in a specific direction.
• Acceleration - is the change in velocity of a period of time. Acceleration
could be positive, negative (retardation) or zero (no change in velocity).
• Force - is a push or a pull which may speed up, slow down, change
direction or shape of an object.
• Energy - is the ability to do work.
• Density - is the amount of matter in a given volume of an object or
substance.
• Moment - is the turning effect of a Force.
• Power - is the rate at which work is done.
• Work - is a force of 1 N displacing an object by 1 m in the direction of the
force.
• Momentum - is the quantity of motion of a moving body, measured as a
product of an object's mass and velocity.
• Pressure - is the force acting on a surface per unit area.

27. Derive quantities

28. Supplementary Quantities
• They are geometrical quantities of circle and
sphere such as plane angle and solid angle.
Similarly, their units not classified as base or
derived units.

29. • Measurement is a process of detecting an unknown physical
quantity by using standard quantity.
• No measurement is exact; there is always some
uncertainty due to
• limited instrument accuracy (systematic error)
• difficulty reading results (random/human error).
• Experiments are NEVER 100% accurate.
– Always have uncertainty in final result.
There are two types of measurement errors:
• Random Errors
• Systematic Errors
Measurement and Uncertainty; Significant Figures

30. Random Errors
• Random errors are statistical fluctuations (in either direction) in
the measured data due to the precision limitations of the
measurement device. Random errors usually result from the
experimenter's inability to take the same measurement in
exactly the same way to get exact the same number.
For Example :You measure the mass of a ring three times using the
same balance and get slightly different values: 17.46 g, 17.42 g,
17.44 g.
• How to minimize it
• Take more data. Random errors can be evaluated through
statistical analysis and can be reduced by averaging over a large
number of observations.
Measurement and Uncertainty; Significant Figures

31. Systematic error
• systematic error is consistent, repeatable error associated with faulty
equipment or a flawed experiment design. These errors are usually
caused by measuring instruments that are incorrectly calibrated or are
used incorrectly.
• A worn out instrument. For example, a plastic tape measure becomes
slightly stretched over the years, resulting in measurements that are
slightly too high,
• An incorrectly calibrated or tared instrument, like a scale that doesn’t
read zero when nothing is on it,
• A person consistently takes an incorrect measurement. For example,
they might think the 3/4″ mark on a ruler is the 2/3″ mark.
• How to minimize it
• Systematic errors are difficult to detect and cannot be analyzed
statistically, because all of the data is off in the same direction(either to
high or too low). Spotting and correcting for systematic error takes a lot
of care. Add or subtract known error.
Measurement and Uncertainty; Significant Figures

32. Preventing Errors
• Random error can be reduced by:
• Using an average measurement from a set of
measurements, or
• Increasing sample size.
• systematic error is difficult to detect — and
therefore prevent. In order to avoid these types
of error, know the limitations of your equipment
and understand how the experiment works. This
can help you identify areas that may be prone to
systematic errors.
Measurement and Uncertainty; Significant Figures

33. • True value – standard or reference of known value or a
theoretical value.
• Accuracy: This is the closeness of the measured
values to the true value.
• Precision: reproducibility or agreement with each other
for multiple trials. It is the closeness of the measured
values to each other: the closer they are to each other,
the more precise they are.
• Uncertainty: The interval in which the true value lies is
called the uncertainty in the measurement.
• Absolute Uncertainty or ± value
• The absolute uncertainty in the mean value of
measurements is half the range of the measurements.
Some terminology

34. Error calculation of Uncertainty
• E.g.
• Suppose the measurements of the diameter of a pin by
a Vernier Caliper are as follows:
• 0.25mm; 0.24mm;0.26mm; 0.23mm;0.27mm;
• Solution
• The mean = (0.25 + 0.24 + 0.26 + 0.23 + 0.27)/5 =125/5
= 0.25mm
• The range = 0.27 - 0.23 = 0.04mm
• Absolute Uncertainty = ± 0.04/2 = ± 0.02
• So, the mean value = mean ± range/2
= 25 ± 0.04/2
= 25 ± 0.02

35. Combining uncertainties + and -
• Adding or subtracting quantities then sum all
individual absolute uncertainties
• eg 2.1 ± 0.1 + 2.0 ± 0.2 = 4.1 ± 0.3
• eg 2.1 ± 0.1 - 2.0 ± 0.2 = 0.1 ± 0.3
this method overestimates the final uncertainty
Error calculation of Uncertainty

36. Rule: percentage uncertainty are added
Estimated uncertainty is written with a ± sign;
for example: 8.8 ± 0.1 cm
Percent uncertainty is the ratio of the uncertainty
to the measured value, multiplied by 100:
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Error calculation of Uncertainty

37. When Dividing or multiplying quantities, then sum all of
the individual relative uncertainties
• eg (2.5 ± 0.1) x (5.0 ± 0.1)
• = (2.5 ± 4%) x (5.1 ± 2%) =12.5 ± 6% (or 0.75 or 0.7)
• eg (5.2 ±0.1) / (0.84 ± 0.05)
• 5.2/0.84 =6.19 = 6.2
• Find % uncertainty: (0.1/5.2)x100 = 1.92 = 2
• (0.05/0.84)x100 = 5.95 = 6
• Sum of % uncertainty = 2%+6% = 8%
• Absolute uncertainty =(8/100)x6.2=0.496 =0.5
• = 6.2 ± 0.5 or 6.2 ± 8%
Error calculation of Uncertainty

38. Significant Figures
The rules of significant figures:
1. Any figures that is non-zero, are considered as a
significant figure.
2.Zeros at the beginning of a number are notsignificant
Example: 0.254 ----------------- 3 s.f
3.Zeros within a number are significant.
Example: 104.6 m ---------------- 4 s.f
4. Zeros at the end of a number after the decimal pointare
significant.
Example: 27050.0 ------------------- 6 s.f

39. • 5. Zeros at the end of a whole number without a decimal point
may or may not be significant.
• It depends on how that particular number was obtained,using
what kind of instrument, and the uncertaintyinvolved.
•Example:500m ------------------- could be 1 or 3sf.
Convert the unit:
• 500m = 0.5km (would you say it has 1 sf ? )
• 500m = 50 000cm (would you say it has 1 or 5 sf ?)
How to solve this problem ?
Significant Figures …

40. Addition and Subtraction processes
The rule:
• The final result of an addition and/or subtraction
should have the same number of significant
figures as the quantity with the least number of
decimal places used in the calculation.
• Example:
• 23.1 + 45 + 0.68 + 100 = 169
• Example:
• 23.5 + 0.567 + 0.85 = 24.9
Significant figures

41. Multiplication and division processes
The rule:
• The final result of an multiplication and/or division
should have the same number of significant figures
as the quantity with the least number of significant
figures used in the calculation.
• Example:
• 0.586 x 3.4 = 1.9924
= 2.0
• Example:
• 13.90 / 0.580 = 23.9655
= 24.0
Significant figures

42. Percentage Error
This is the formula for "Percentage Error":
Example: The report said the carpark held 240
cars, but we counted only 200 parking spaces.
What is the percentage error in the report.

43. Exercise
1) You measure a block with a ruler that has a precision of 1mm. You
obtain a length of 2.4cm.
• a) What is the absolute uncertainty in this measurement?
• b) What is the percentage uncertainty in this measurement?
2) The following range of results is obtained for the mass of a bouncy
ball: 13.2g, 13.4g, 13.3g, 13.4g, 13.2g, 13.3g
• a) Calculate a value for the mass of the bouncy ball.
• b) What is the absolute uncertainty in these measurements?
• c) What is the percentage uncertainty in these measurements?

44. • 3. How many Significant figures in each term?
a. 34.6209
b. 0.003048
c. 5010.0
d. 4032.090
4.Solve the following equations using the correct number of
significant figures.
a. 34.683 + 58.930 + 68.35112
b. 45001 - 56.355 - 78.44
c. 0.003 + 3.5198 + 0.0118
d. 36.01 - 0.4 - 15
5.Solve the following equations using the correct number of
significant figures.
a. 98.1 x 0.03
b. 57 x 7.368
c. 8.578 / 4.33821
d. 6.90 / 2.8952
Exercise

45. • 6. A builder wants to calculate the area of a square tile.
He uses a rule to measure the two adjacent sides of a
square tile and obtains the following results: Length of
one side = 84 mm ± 0.5 mm Length of perpendicular
side = 84 mm ± 0.5 mm.
• 7. A metallurgist is determining the purity of a sample
of an alloy that is in the shape of a cube by
determining the density of the material. The following
readings are taken: Length of each side of the cube=
24.0 mm ± 0.5 mm Mass of cube = 48.23 g ± 0.05 g She
calculates (i) the density of the material and (ii) the
percentage uncertainty in the density of the material.
Exercise

46. • 8. A bullet travels a distance of l=154±0.5 m in
the time t=0.4±0.05 s.
• a) Calculate the fractional uncertainty for the
speed of the bullet.
• b) Calculate the percentage uncertainty for the
speed of the bullet.
• c) Write down the speed of the bullet using the
absolute uncertainty.
Exercise

47. Exercise
• 9. A ball is thrown in the air and 5 different
students are individually measuring the time it
takes to fall back down using stopwatches.
The times obtained by each student are the
following:
6.2 s, 6.0 s, 6.4 s, 6.1 s, 5.8 s
• a) What is the uncertainty of the results?
• b) How should the resulting time be
expressed?

48. exercise
• 10. The current passing through a resistor is
I=3±0.1 A and the resistance of the resistor is
R=13±0.5 Ω. The electrical power, measured in
watt (W), supplied to the resistor is given by P=RI2.
• a) Write down the value of the supplied power
correct to one significant figure.
• b) Find the percentage uncertainty for the current
passing through the resistor and its resistance.
• c) Find the absolute uncertainty for the electrical
power.

49. DIMENSIONS
AND
DIMENSIONALANALYSIS