Physics, Fundamental and Derived Quantities and Units

TOPIC: INTRODUCTION TO PHYSICS

CONTENT

• MEANING OF PHYSICS
• FUNDAMENTAL QUANTITIES AND UNITS
• DIMENSIONS OF PHYSICAL QUANTITIES

MEANING OF PHYSICS

Physics is the scientific study of matter and energy and how they interact with each other. This energy can take the form of motion, light, electricity, radiation, gravity etc. Physics deals with matter on scales ranging from sub-atomic particles (i.e. the particles that make up the atom and the particles that make up those particles) to stars and even the entire galaxies. It can also be defined as a natural science that involves the study of matter and its motion through space-time, as well as all applicable concepts, such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.

Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, Physics had been considered synonymous with Philosophy, Chemistry, and certain branches of Mathematics and Biology, but during the scientific revolution in the 16th century, it emerged to become a unique modern science in its own right. However, in some subject areas such as in mathematical physics and quantum chemistry, the boundaries of physics remain difficult to distinguish.

Physics is both significant and influential, in part because advances in its understanding have often translated into new technologies, but also because new ideas in Physics often resonate with other sciences, Mathematics, and Philosophy. For example, advances in the understanding of electromagnetism or Nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of motorized transport; and advances in mechanics inspired the development of calculus.

In order to understand clearly the fundamental concepts, Physics is divided into two main branches:

• Classical Physics – This consists of the following: mechanics, heat, optics, wave and sound, electricity and magnetism.
• Modern Physics – This covers the aspects of matter energy and their relations at atomic and sub-atomic levels.

Other fields of Physics are: Geophysics, Astrophysics, Bio-physics, Nuclear physics, Engineering physics etc.

EVALUATION

1. What do you understand by the term “Physics’’?
2. State the step involved in scientific method?

FUNDAMENTAL QUANTITIES AND UNIT

Measurements play an important role in Physics. A unit has to be defined before any kind of measurement can be made.  Different systems of units have been used in the past. These include the foot – pound – second (FPS) system, the centimetre – gramme – second (CGS) system, and the metre – kilogramme – second (MKS) system. The new system which has now gained universal acceptance is the systeme international d’units, usually called S.I. units.

Physical quantities are often divided into fundamental quantities and derived quantities.

FUNDAMENTAL QUANTITIES:

These are the basic quantities that are independent of others and cannot be defined in terms of other quantities.

They are the basic quantities upon which most (though not all) quantities depend.

FUNDAMENTAL UNITS: are the basic unit upon which other units depend. They are the units of the fundamental quantities.

The three most important basic quantities in Physics are length, mass and time.

Length may be defined as the extent of space or distance extended.

Mass is commonly defined as the quantity of matter or material in the body.

Time is defined as that in which events are distinguishable with reference to before or after. Examples of fundamental quantities and their units are shown below:

Table 2.0 Fundamental Quantities and Units

DERIVED QUANTITIES AND UNITS

Derived quantities and units are those obtained by some simple combination of the fundamental quantities and units. They are dependent on the fundamental quantities and units. Some examples of derived quantities and units are shown below:

Table 2.1 derived quantities and units

The unit of volume is obtained by multiplying three lengths m x m x m = m³ pronounced ‘CUBE METRE” or “METRE CUBED”. Density is the ratio of mass and volume therefore the unit of density is kg/m³ or kgm^-3 pronounced “KILOGRAMME PER METRE CUBED.”

Difference between Fundamental and Derived Units

Difference between Fundamental and Derived Quantities

DIMENSIONS OF PHYSICAL QUANTITIES

The dimension of a physical quantity is the way it is related to the quantities of mass, length and time. The dimension of unit mass is M, for unit length, L and for unit time T. see the table below:

Table 2.2

DIMENSION ANALYSIS OF SOME PHYSICAL QUANTITIES

• Density: This is mass  per unit volume
  The dimensional equation of density = dimension of mass/dimension of volume

                                                      = kg/m^3 = M/L^3 = ML^-3

• Velocity: This is the rate of change of displacement with time.

Velocity = dimension of displacement/dimension of Time  = m/s = L/T = LT^-1

• Acceleration: This is the rate of change of velocity with time.

Acceleration = dimension of velocity/dimension of time   = kg/m^3 = M/L^3 = ML^-3

• Force: This is the product of mass and acceleration.

= Dimension of mass x Dimension of acceleration

= kg × ms^-2

= m × LT^-2

= MLT^-2

Below is a table of a few important physical quantities and their dimensions:

Table 2.3

EVALUATION

1.         State the dimension of the following quantities;

            (a) Acceleration (b) pressure (c) density

2          From the following quantities given below, list out the derived and fundamental quantities in a   tabular form: Velocity, mass, weight, length, volume, density, torque, speed, acceleration, power, energy, temperature, heat capacity, electric current, relative density

Reading Assignment

New school physics by M.W.Anyakoha, Prof. Pg1-2

WEEKEND ASSIGNMENT

1.         Which of the units of the following physical quantities is not derived unit?

            (a) Area            (b) Thrust        (c) Pressure      (d) Mass

2.         Which of the following is a fundamental unit?  (a) Kgm⁻³         (b) m3 (c) Nm⁻²          (d)  Kg

3           Which of the following quantities has the same unit as energy?

            (a) Power         (b) Work          (c) Force          (d) Momentum            

4          Which of the following is a derived unit?

            (a) Ampere       (b) Kilogramme            (c) Second       (d) Ohm

5          Which of the following is a derived unit?

            (a) Tension       (b) Impulse      (c) Upthrust     (d) Distance

6.         The international agreed system of unit (S.I.) for physical measurement are

            (a) lb, ft, sec    (b) g, m, sec    (c) kg, m, sec   (d) cm, g, sec

7.         Which of the units of the following physical quantities are derived?

            I. Area; II. Thrust;        III. Pressure;    IV. Mass

            (a) I, II, III and IV       (b) I, II and III only     (c) I, II and IV only      (d) I and IV only

THEORY

1.         State the dimension of the following;

            (a) stress(Force/Area) (b) Energy(force x perpendicular distance)

            (c) Momentum (mass x velocity)

2           Determine the dimension of the following physical quantities.

(a) Impulse      (b) potential energy     (c) pressure     (d) young’s modulus

3      At what respective value of a, b, and c would the unit of impulse be dimensionally equivalent to    M^aL^bT^c?

4.         The dimension of pressure is given as M^xL^yT^z, deduce the values of x, y, and z. (Hint: Pressure= Force/Area, the unit is Nm^-2)