User:Chris Nwachioma

Introduction to Contemporary Physics

INTRODUCTION

For the record, let it be known that Physics covers two broad area – namely:

Classical Physics, and
Quantum Physics

CLASSICAL PHYSICS: otherwise known as the Newtonian Physics is the Physics in which the object of study is macroscopic or large enough to be visible to the eyes using ordinary light. Objects that falls within this category are affected by the gravitational field. Examples of classical objects are man, moon, sun, planets, vehicles, aeroplane, shoe, rice grain, guns, bullets, etc.
QUANTUM PHYSICS: in Quantum Physics, the objects of study are microscopic or small enough not to be visible to the eyes using ordinary light through a simple microscope. These objects are of atomic dimensions or less and may only be visible using a sophisticated electron microscope. We know they exist because we see their effects in several scientific inventions and innovations. Examples of quantum objects (or particles) are electrons, quarks, bosons, higgs bosons. In quantum Physics, the concept of path (or trajectory) is meaningless.

Throughout this text, we shall dwell mainly on the Classical Physics.

UNITS AND MEASUREMENTS

Physics, as an experimental science, requires measurement. The values of measurements are recorded as numbers (or physical quantities). Those numbers or quantities that cannot be calculated from other quantities, that is, they are only measured using rulers, stopwatches, and what have you are called fundamental quantities. There are 7 fundamental quantities of nature and they are discussed below.

7 FUNDAMENTAL QUANTITIES OF THE PHYSICAL WORLD

Fundamental Quantity are those measurable quantities of our physical world that are NOT derived. They are fundamental or basic to defining other physical measurable quantities. The fundamental quantities of Physics are:

Time: is a dimension that represents a succession of events. The precise determination of time rests on astronomical and atomic definitions that scientists have established with the utmost mathematical exactness. For non-relativistic (low speed) classical Physics, time behaves as an absolute quantity, that is, it is the same for everyone irrespective of their different frames of reference (or different platform of motion of variable speeds).
WAYS OF MEASURING TIME
1. Solar Time: is based on the rotation of the earth round its axis. It makes use of the sun’s apparent motion across the sky to measure the duration of the day.
2. Sidereal Time: like the solar time is based on the earth’s rotation but uses the apparent motion of the fixed stars across the sky as the earth rotates as the basis for time determination. Note that the sidereal day is 4 minutes shorter than the mean solar day.
3. Standard Time: is the familiar clock time most of us use everyday. It is based on the division of the earth’s sphere into 24 equal time zones. This implies that having 24hours in a day is our choice. Had we wanted 48hours in a day, we would have divided the earth’s sphere into 48 equal time zones and in this case an hour will be as long as our today’s 30-minute.
4. Dynamic Time (formerly called Ephemeris Time) – is the timescale of astronomy. Astronomers use the earth’s orbit around the sun, as well as orbital motions of the moon and other planets to determine dynamical time.
5. Atomic Time: is based on the frequency of electromagnetic waves (e.g. light) that are emitted or absorbed by certain atoms or molecules under particular conditions. This is the most precise method of measuring time. Generally, the SI (système internationale) unit of time is the second (s). Since the second is a unit of the fundamental quantity, time, it is called a fundamental unit.
Definition of the second
The second, the basic unit of time, was defined as 1/86,400 of a mean solar day. Later, scientists discovered that the rotation of the earth was not steady enough to be used as the basis of time standard. Hence, a new definition of the second was given in 1967. Second was defined as the frequency at which caesium atom absorbs energy, or 9,192,631,770 hertz (cycles per second).
Length: the distance along an object measured from one end to the other. The SI unit of length is the meter (m). Meter is a fundamental unit since it is the dimension of a fundamental quantity. The following are the various definitions of meter. 1. The length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second (1983 definition) 2. 1,650,763.73 wavelengths of the reddish-orange light emitted by the isotope krypton-86 (1960 definition) 3. By international agreement, the standard meter is defined thus, the distance between two fine lines on a bar of platinum-iridium alloy.
Mass: this is defined as the quantity of matter in an object. The SI unit of mass is the kilogram (kg). The following are the definitions of the kilogram. 1. The kilogram was defined as the mass of 1 cubic decimetre (dm3) of pure water at the temperature of its maximum density (4.0° C or 39.2° F). Later, it was discovered that a quantity of water as pure or as stable as required could not be provided; hence, a solid cylinder of platinum-iridium was carefully made to match this quantity of water under some specified conditions. Till date, this cylinder serves as the international kilogram. 2. From the foregoing, a better definition of a kilogram is thus, the quantity of mass in the international platinum-iridium cylinder.
Temperature: is a measure of the degree of hotness or coldness of a body relative to another. The SI unit of temperature is the Kelvin or Celsius.
Electric Current: this is the flow of electricity through a conductor. The SI unit is the Ampere.
Luminous Intensity: is the amount of light emitted by a source in a particular direction. The SI unit of luminous intensity is the candela. The candela is defined most precisely as the intensity of a light source, in a given direction, with a frequency of 540 x 1012 hertz and a radiant intensity of 1/683 watts per steradian in that direction.
Amount of substance: the SI unit is the mole. It is the amount of substance of a system that contains as many elementary entities as there are in 12g (0.012kg) of carbon-12.

Table showing the fundamental quantities, their SI units and symbols

S/N	FUNDAMENTAL QUANTITIES	SI UNITS	SYMBOLS
1.	Time	Seconds	s
2.	Length	Meter	m
3.	Mass	Kilogram	kg
4.	Temperature	Celsius, or Kelvin	⁰C, or ⁰F
5.	Luminous Intensity	Candela	Cd
6.	Electric Current	Ampere	A
7.	Amount of Substance	Mole	mol

DERIVED QUANTITIES AND UNITS

Derived quantity are those measurable quantities (or observables) of the physical world that are gotten from or dependent on at least two (but not necessary separate two) of the fundamental quantities. Examples of derived quantities are speed, area, volume, acceleration, force, moment, momentum, heat capacity etcetera. Their SI units are a mixture of two or more of the fundamental units. For instance, the SI units of the following quantities are written next to each of them in a bracket beside them. Force (kgm/s²), area (m²), volume (m³), speed (m/s), acceleration (m/s²), heat capacity (m²/s²kg.K). Note: the derived units stated above, are stated dimensionally and each is expressed in terms of the fundamental units (discussed above)

UNITS CONVERSIONS

S/N	TIME	LENGTH	MASS
1.	1 nanosecond = 1 ns = 10^-9 s	1 nanometer = 1 nm = 10^-9 m	1 microgram = 1µg = 10^-6 g = 10^-9kg
2.	1 microsecond = 1 µs = 10^-6 s	1 micrometer = 1 µm = 10^-6 m	m
3.	1 millisecond = 1 ms = 10^-3 s	1 millimeter = 1 mm = 10^-3 m	kg
4.	1 hour = 1 hr = 3600 s	1 centimeter = 1 cm = 10^-2 m	⁰C, or ⁰F
5.	24 hours = 86400 s	1 kilometer = 1 km = 1000 m	Cd

1 gram = 1 g = 10-3 kg

2. Temperature Conversions a) Degree Celsius (0C) to Kelvin (K)

X 0C = (x + 273.15) K

b) Degree Celsius (0C) to Fahrenheit (F)

TC = 5/9 (TF – 320) Where TC is temperature in degree Celsius, TF is temperature in Fahrenheit.

EXERCISE 1.0 Try the exercise yourself. Compare your results with the solutions in the next page. 1. Convert the following fundamental quantities to their SI units’ equivalents. a) 24 km b) 1.5 hr c) 6,000,000,000 µg d) 0.05 km 2. Convert the following derived quantities to SI units. a) 30 km/hr b) 0.05 g/mol c) 360 cm/minute d) 140F 3. Give the most current and standard definition of the following. a) Time b) Length c) Mass d) Temperature e) Candela f) Mole 4. Pick the odd one out. a) Mass b) Luminous intensity c) Meter d) Temperature e) Amount of substance Solutions to EXERCISE 1.0 1. Refer to units conversions on section 1.12 a) 24 km = 24 km (1000 m) = 24,000 m b) 1.5 hr = 1.5 hr (3600 s) = 5,400 s c) 6,000,000,000 µg = 6,000,000,000 µg ( )( ) = 6 kg d) 0.05 km = 0.05 km ( ) = 50 m 2. Solution a) 30 km/hr = ( )( )( ) = 81/3 m/s b) 0.05 g/mol = ( )( ) = 0.00005 kg/mol c) 360 cm/min = ( )( )( ) = 0.06 m/s d) 140F to degree Celsius. TC = 5/9 (TF – 320) TC = 5/9 (14 – 32) TC = 5/9 x – 18 TC = 5 x -2 TC = -100C 3. Definitions a) Time: is a dimension that represents a succession of events. b) Length: is the distance between two fine lines on a bar of platinum-iridium alloy. c) Mass: is the quantity of matter in a body. d) Luminous intensity: is the amount of light emitted by a source in a particular direction. e) Candela: it is the SI unit of luminous intensity. It is defined as the intensity of a light source, in a given direction, with a frequency of 540 x 1012 hertz and a radiant intensity of 1/683 watts per steradian in that direction. f) Temperature: is a measure of the degree of hotness or coldness of a body relative to another. g) Mole: a mole is the amount of substance of a system that contains as many elementary entities as there are in 12g (0.012kg) of carbon-12. 4. The ODD ONE is the meter because, while it is a fundamental unit, the rest are fundamental quantity. EVALUATIONS 1. Define the following. a) Solar time b) Sidereal time c) Standard time d) Dynamic time e) Atomic time. 2. Which in 1 above, gives the most accurate time? 3. What do you understand by the following? a) Fundamental quantity b) Derived quantity c) Fundamental unit d) Derived unit 4. Give the most precise definition of the following. a) Second b) Meter c) Kilogram d) Candela KINEMATICS This is the study of the motion of an object without reference to the mass of the object or force producing the motion. To do a proper study of this kind of motion, we shall describe an object using the following variables. 1. Speed 2. Acceleration 3. Time 4. Distance Average Distance The average distance covered by an object in uniform motion is defined as follows. Sav =1/2(v0 +v) Average speed The average speed for an object in motion is given by the following. <v> = ∆⅟⅟⅔