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Education is what remains after one has forgotten what one has learned in school. . I have no special talent. I am only passionately curious. . It's not that I'm so smart, it's just that I stay with problems longer. .

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Education is what remains after one has forgotten what one has learned in school.

I have no special talent. I am only passionately curious.

It's not that I'm so smart, it's just that I stay with problems longer.

Most people say that is it is the intellect which makes a great scientist. They are wrong: it is character.



The goal of physics is to gain deeper understanding of the world in which we live. Physics is the study of the fundamental laws of nature. It is concerned with the basic principles of the Universe and is foundation on which the other physical sciences – astronomy, chemistry … - are based.

Remarkably, we have found that these laws can be expressed in terms of mathematical equations. As a result, it is possible to make precise, quantitative comparisons between the predictions of the theory-derived from the mathematical form of the laws – and the observations of experiments.


The small number of basic concepts, equations, and assumptions can alter and expand our view of world.


Theories themselves are generally not perfect. History of science tells us that theories come and go. Many times theory is satisfactory under certain limited conditions. Usually the new theory is accepted when its predictions are quantitatively in much better agreement with experiment than those of the older theory, but even more important is that it can explain a greater variety of phenomena than does the older one.

No amount of experimentation can ever prove me right;

a single experiment can prove me wrong.

Example: Newtonian mechanics – accurate description of motions of objects moving at speeds small compared to the speed of light.

Limitation: it cannot successfully describe fast moving small particles.

A more general theory of motion without that limitation:

Special theory of relativity – Albert Einstein.

Quantitative aspect: In nearly all everyday situations, Einstein’s theory

gives predictions almost the same as Galileo’s and Newton’s.

Main distinction is in extreme case of very high speed

(close to the speed of light)

Qualitative aspect: Our view of the world is affected with that theory.

– Our concepts of space and time underwent a huge change

– mass and energy as a single entity ( E = mc2 ).


Robert J. Sciamanda, Edinboro University of Pennsylvania

No physicist or engineer ever solves a real problem. Instead she/he creates a model of the real problem and solves this model problem. This model must satisfy two requirements: it must be simple enough to be solvable, and it must be realistic enough to be useful; ie., it must be both conceptually understandable and empirically fruitful.

The theories and "laws" of physics are also models. Whether in the solving of a particular engineering problem or in the search for the wide ranging laws of physics, the art of scientific analysis consists in the creation of useful models of reality. The model is the interface between reality and the human mind. As such, the model must be expressed in human terms; it is cast in terms of concepts which we create from the data of our experience. Our models speak as much about us, our experience and our modes of thought as they do about the external reality being modeled.


Theory is when you know something, but it doesn’t work.

Practice is when something works, but you don’t know why.

(Albert Einstein)

Programmers combine theory and practice: Nothing works and they don’t know why.


The difference between theory and practice is that in theory there is no difference, but in practice there is.

(Craig A. Finseth)



We know everything about the motion if we know the position and the velocity of that object at any time.

Motion of an object can be very complicated

Question: Do all points on the ball follow the same path at the same time?

Is head at the same position as the wheels?

Do legs follow the same path as the head?

The simplest model: we choose to ignore everything that is not important (color) or too complicated (shape, size, spin, air resistance)

Look at the center of mass of the hammer.

The path is very simple: parabola


click me

Simplifying complicated situations: the system we are

going to study will be treated as POINT OBJECTS

– so shape, no size, no spin, no relative motion of the body parts

Point Object: - imagine the center of mass of the car or hammer and imagine that we squished the car or hammer so that the whole mass is concentrated at that point

– we draw the whole object it as a small circle and we call it: a point object (surprise).


All physical phenomena in our world are more or less successfully described in terms of one or more of the following theories:

  • Classical mechanics – study of matter, motion, forces and energy.

It describes the motion of the objects that are

1. large compared with the dimensions of atoms (10-10 m)

2. moving at speeds that are low compared to the speed of light (3x108 m/s)

  • Relativity - describing particles moving at any speed, even those whose

speed approach the speed of light;

  • Thermodynamics, which deals with heat, temperature,

and the behavior of large numbers of particles;

  • Electromagnetism, which involves the theory of electricity,

magnetism, and electromagnetic fields;

  • Quantum mechanics, a theory dealing with the behavior

of submicroscopic particles.


Range of magnitudes of quantities in our universe

Only two things are infinite, the universe and human stupidity, and I'm not sure about the former.

click me!

click me!

Physics tries to explain everything in universe from very large to very small.

visible universe is thought to be around 1025 m.

age of the universe is about 1018 s.

estimated total mass of the universe is around 1050 kg

diameter of an atom is about 10-10 m.

diameter of a nucleus 10-15 m.

If an atom were as big as a football field nucleus would be about the size of a pea in the centre.

Conclusion: you and I and all matter consists of entirely empty space.


Elegance in physics:

We use Scientific Notation or Prefixes when dealing with numbers that are very small or very big.


The best current estimate of the age of the universe is

13 700 000 000 = 13.7 × 109 years = 13.7 billion years

scientific prefix


2.electron mass = 0.000 000 000 000 000 000 000 000 000 000 91 kg

= 9.1 × 10-31 kilograms

3. 0.00354 m = 3.54 x 10-3 m = 3.54 mm



The ones that should be remembered:

every step is 10±3 power


Dimensional Analysis

When doing physics problems, you'll be required to determine the numerical value and the units of a variable in an equation.

Anything you measure or calculate in physics

Physical quantities are expressed in UNITS


We will use

The International System of Units

(abbreviated SI from French: Système international d'unités) is the modern form of the metric system adopted in 1960. SI systemis the world's most widely used system of units, used in both everyday commerce and science.

Dimensions aren't the same as units. For example, the physical quantity, speed, may be measured in units of meters per second, miles per hour etc.; but regardless of the units used, speed is always a length divided a time, so we say that the dimensions of speed are length divided by time, or simply L/T. Similarly, the dimensions of area are L2 since area can always be calculated as a length times a length.


Dimension of physical quantity distance is length.

Dimension of speed is length/time


ALL physical quantities can be expressed in terms of combinations of seven basic /fundamental dimensions. These seven dimensions have been chosen as being basic because they can be measured directly.

Derived dimensions/physical quantities require the measurement of more than one dimension/quantity.


Some Derived


of Unit




of Unit








In the study of mechanics, we shall be concerned with physical quantities/dimensions

  • (and units) that can be described in terms of three dimensions:
  • length (L), time (T) , and mass (M).
  • Thecorresponding basic SI- units are:
  • Length – 1 meter (1m) is the distance traveled by the light in a vacuum during
  • a time of 1/299,792,458 second.
  • Mass – 1 kilogram (1 kg) is defined as a mass of a specific platinum-iridium

alloy cylinder kept at the International Bureau of

Weights and Measures at Sevres, France

  • Time – 1 second (1s) is defined as 9,192,631,770 times the period of one
  • oscillation of radiation from the cesium atom.

1 kg is basic unit of mass,

not, I repeat, not 1g !!!!!!!!!!


Fun with Dimensional Analysis

1. Given the definition of a physical quantity, or an equation involving a physical quantity, you will be able to determine the dimensions and SI units of the quantity.

2. Given an equation, you will be able to determine if the equation is dimensionally correct or incorrect.









Sometimes we give the new name to the derived units.

Example: Find units expressed in basic SI units for

a. force (F = ma, a = v/t)

b. kinetic energy ( KE = ½ mv2 )

a. unit for force = (unit for mass)x(unit for speed/unit for time)

= 1 N (Newton)

b. unit for KE = (unit for mass)x(unit for speed)2

= J (Joule)

½ is number, it cannot be measured → no unit


Determine the dimensions and corresponding SI units of the following quantities:


acceleration (velocity/time)

density (mass/volume)

force (mass × acceleration)

charge (current × time)


pressure (force/area)

work (force × distance)

L3, m3

L/T2, m/s2

M/L3, kg/m3

M•L/T2, kg•m/s2

I•T, A•s

L, m

M/(L•T2), kg/(m•s2)

M•L2/T2, kg•m2/s2


Which one of the following quantities are dimensionless (and therefore unitless)?

1. 68° dimensionless

2. sin 68° dimensionless

3. e dimensionless

4. force not dimensionless

5. 6 dimensionless

6. frequency not dimensionless

7. log 0.0034 dimensionless


Determine if the following equations are dimensionally correct.

1. x = xo + vo t + (1/2) a t2

where x is the displacement at time t, xo is the displacement at time t = 0,

vo is the velocity at time t = 0, a is the constant acceleration

Dimensionally correct. Each term has dimensions of L.

2. P =

where P is pressure, ρis density, g is gravitational acceleration, h is height

Not dimensionally correct.

[P] = M•L-1•T-2 [] = M1/2•L-1/2•T-1

Dimensional correct would be P = ρgh


The equation for drag force in a liquid is:

F = -2r L 


F is force

r is radius

L is length

v is speed

d is distance

What are the dimensions and SI unit of (viscosity)?

A simulation of substances with different viscosities. The substance above has lower viscosity than the substance below

dimension is M•L-1•T-1.

The corresponding SI unit is kg•m-1•s-1.


At the pizza party you and two friends decide to go to Mexico City from El Paso, TX where y'all live. You volunteer your car if everyone chips in for gas. Someone asks how much the gas will cost per person on a round trip. Your first step is to call your smarter brother to see if he'll figure it out for you. Naturally he's too busy to bother, but he does tell you that it is 2015 km to Mexico City, there's 11 cents to the peso, and gas costs 5.8 pesos per liter in Mexico. You know your car gets 21 miles to the gallon, but we still don't have a clue as to how much the trip is going to cost (in dollars) each person in gas ($/person).

I bet that if you found yourself in situation like this one you could do it and travel to Mexico City for $96/person.

Let us do the same thing in physics:

Converting units and prefixes

1. Way – pretty complicated, but widely used

2. Easier way (maybe) – direct conversion – for ratio of units !!!!

3. Your way



1 m = 3.281 ft

316 ft= ? m

316 ft


26.4 m = ? ft

26.4 m ft

26.4 (3.281 ft)ft

4.3 x 104 ns = ?µs

4.3 ns = 43 µs

4.3 s = 43 µs

5.2 x 108ms = ?ks

s = 520 ks

= 520 ks


7.2 m3 → mm3

= 7.2 x

100 mm3 → m3

= 10-7m3

75= 750 kg/m2

75 g/cm2 → kg/m2

20 = 20 = 72 km/h

20 m/s → km/h

72 = 20 m/s

72 km/h → m/s

1 mi = 1609 m

60 = 27 m/s

60 mi/h = ? m/s


Uncertainty and error in measurement

No matter how hard we try, it is never possible to know with absolute certainty that the measurement is perfect.

two types: random and systematic.

Random: readings of a measurement are above and below the true value with equal probability.

usually caused by person making the measurement.

Systematic: readings are off due to the system or aparatus being used.

● an observer constantly making the same mistake.

● apparatus calibrated incorrectly

● zero offset

● can be detected using different methods of measurement.


Another distiction in measurements is between precision and accuracy.

Imagine the game: dart.

precise, not accurate

accurate, not precise

neither precise, nor accurate

both accurate and precise

It is the same with measurements.



is the degree of exactness (or refinement) of a measurement (results from limitations of measuring device used).


is the extent to which a reported measurement approaches the true value of the quantity measured – how close is the measurement to the reality.

I do just the opposite. My head goes to the other side. It shows less so I can have my breakfast in peace.


Distribution of large number of measurements of the same quantity around the correct value of the quantity.


No measurement can be "exact". This would require a measuring instrument with marks infinitely close together - which is clearly impossible.

When certain quantities are measured, the measured values are known only to within the limits of the experimental uncertainty (depending on the quality of the apparatus, the skill of experimenter, ...).

SIGNIFICANT FIGURES are reliably known digits+ one uncertain

52 mL – reliably known

0.8 unceratin – estimate

52.8 mL


☞ All digits 1,2,3…9 count as significant digits.

7 642.95 (6 SF)

About Zeros:

☞ Zeros between other non zero digits are significant.

50.3 (3 SF ), 3.0025 (5 SF)

☞ Zeros in front of non zero digits are NOT significant:

0.67 (2 SF), 00843 ( 3 SF), 0.0008 (1 SF).

Zeros at the beginning merely locate the decimal point.

☞ Zeros to the right of a decimal are significant.

57.00 (4 SF), 2.000 000 (7 SF)

Zeros at the end of a DECIMAL number are significant

(it means: we know that digit is 0)


☞ Zeros at the end of a number are ambiguous.

34 000 m3(2, or 3 or 4 or 5 SF?).

☞ Rule: use scientific notation if you know how many

significant figures there are

for example if this is the result of calculations, and you know

there are only 2 SF, then the result is:

34 000 m3= 34 x 103 m3


Significant digits in a calculation:


Addition or subtraction:

The final answer should have the same number of DECIMALS as the measurement with the smallest number of decimals.

2.2 + 1.25 + 23.894 = 27.164 → 27.2




27.164 → 27.2

you don’t know second decimal in the first measurement and third decimal in second measurement, so the result can not have reliably known second and third decimal.

97.329 - 47.54 = (49.789) = 49.80

(3 dec) - (2 dec)= (2 dec)

Answer should be reported with 2dec only


Multiplication, Division, Powers and Roots:

The final answer should have the same number of SIGNIFICANT DIGITS as the measurement with the smallest number of significant digits

Ex: 121.30 x 5.35 = (648.955) = 649

(5 SF) x (3 SF) = = (3SF)

Answer should be rounded up to 3 SF only