UNITS, FUNDAMENTAL TERMS & DEFINITIONS

Derived units of ‘SI’ units:

SN	Quantity	Name of SI units	Unit symbol
1	Area (A)	Square metre	m2
2	Volume (V)	Cubic metre	m3
3	Velocity (V)	Metre per second	m/s
4	Angular Velocity (ω)	Radian per second	rad/s
5	Acceleration (α)	Metre per second square	m/s2
6	Angular acceleration	Radian per second square	rad/s2
7	Density (D)	Kilogram per cubic metre	Kg/m3
8	Force (F)	Newton	N=kgm/s2
9	Torque, Moment of force, Bending moment, Moment of couple (T)	New-metre	N-m
10	Moment of inertia (dynamic)	Kilogram metre square	Kgm2
11	Specific weight (specific density)	Newton per cubic metre	N/m3
12	Pressure, Normal Stress, Shear stress, Shear modulus, Bulk modulus (P)	Newton per square metre	N/m2
13	Dynamic viscosity	Newton second per square metre	Ns/m2
14	Kinematic viscosity	Square metre per second	m2/s
15	Work, Energy, Quantity of heat (E)	Joule	J=Nm
16	Power, Heat flow rate (P)	Watt	W=J/s
17	Thermal conductivity	Watt per metre Kelvin	W/mK
18	Co-efficient of heat transfer	Watt per square metre Kelvin	W/m2K
19	Specific heat capacity	Joule per kilogram Kelvin	J/kg K
20	Frequency, Rotational frequency (f)	Hertz	Hz
21	Wave length	Metre	m
22	Luminous flux (Ф)	Lumen	lm==(cd-sr)
23	Illumination (E)	Lux	lx=(lm/m2)
24	Brightness or Luminance (L)	Candela per square metre	cd//m2
25	Charge of quantity of electricity (Q)	Coulomb	C=As
26	Electric potential, Potential difference, e.m.f. (V,E)	Volt	V=W/A
27	Electric field strength (E)	Volt per metre	V/m
28	Resistance  (R)	Ohm	Ω=V/A
29	Capacitance (C)	Farad	F=C/V
30	Inductance (L)	Henry	H=Wb/A
31	Magnetic flux (φ)	Weber	Wb=Vs
32	Magnetic flux density (B)	Tesla	T=Wb/m2
33	Magnetic field strength (H)	Ampere per metre	A/m
34	Magneto motive force (F)	Ampere turn	A.T

International ohm: It is the resistance offered to an unvarying current by a column of mercury 106.3 cm, 1 mm² cross section and weight 14.4521 gm at the temperature of melting ice.

International ampere: It is that steady current which, in flowing through a specified solution of silver nitrate (AgNO₃), deposits silver on the cathode the rate of 0.0001118 gm/sec.

International volt: It is that steady e.m.f. which, applied to the ends of a conductor whose resistance is 1 international ohm causes a current of 1 international ampere to flow.

International watt: It is the electrical energy expanded per second to a circuit if the current in it is 1 international ampere and the pressure across it is 1 international volt.

Matter: Matter is anything which occupies space and can affect one or more of our senses.

Mass: Mass is the quantity of matter contained in the body which does not alter at any place as it is not affected by the force of attraction of the earth.

Weight: The force of attraction of the earth on a given mass is the weight of that mass.

Speed: Speed is the rate of change of motion of a particle in any direction. It is a scalar quantity. It is expressed in unit distance in unit time uniformly such as ft/sec, cm/sec, metre/sec, km/hour, miles/hour etc.

Velocity: Velocity is the rate of motion in a given direction measured as length per unit time. It is a vector quantity.

Difference between speed & velocity:

i)                    Speed is a scalar quantity but velocity is a vector quantity.

ii)                  Speed has no definite direction but velocity has a given definite direction.

iii)                Speed is always positive but velocity can be both positive and negative.

iv)                Uniform speed does not necessarily guarantee uniform velocity but uniform velocity guarantees uniform speed.

Acceleration & Retardation: The rate of change of velocity is called acceleration. The positive acceleration i.e. when the velocity increases regularly, generally termed as acceleration and the negative acceleration i.e. when the velocity decreases regularly, it is termed as retardation.

Force: Force is an external agency capable of altering the state of rest or uniform motion in a body. SI unit of force is ‘Newton’.

Moment: Moment of force is a measure of the tendency of a force to rotate the body to which it is applied. It is measured by multiplying the magnitude of the force by the perpendicular distance from the line of action of the force to the axis of rotation.

Torque: Torque is the twisting moment imparted to a body to give it a circular motion. SI unit of torque is ‘Newton-metre. The torque is measured by the product of the force and the perpendicular distance from the line at which the force acts.

Momentum: Momentum is the product of the mass and the velocity of a body.

Work: Work is said to be done by a force, when that force acting on a body moves the body through certain distance. It is measured as the product of the force and the distance through which the body moves in the direction of the force applied.

Power: Power is the rate of doing work. The electrical unit of power is watt, the bigger unit is Kilowatt, the mechanical unit of power is Horse Power (H.P.). The rate of working of 33000 ft-lb per minute or 550 ft-lb per second or 4500 kg-m per second is known as one horse power.

1 H.P.(British) = 746 Watts

1 H.P.(Metric) = 735.5 Watts

Energy: Energy of an agent is  its capability of doing work. Small unit of electrical energy is Watt-sec. For commercial purpose the unit of electrical energy is Watt hours and Kilo Watt hours (kWh). The kWh is also known as Board of Trade Unit (B.O.T.) unit.

                 Volt x Ampere x Time in hours

kWh     = ----------------------------------------                   Energy =  Power x Time

                                      1000

Types of Energy:

1)      Mechanical Energy

2)      Thermal Energy

3)      Light Energy

4)      Sound Energy

5)      Electrical Energy

6)      Chemical Energy

7)      Nuclear Energy

Heat: Heat is the energy possessed by a substance in the form of kinetic energy of atomic or atomic or molecular translation, rotation or vibration which produces a sensation of hotness.

Kilo Calorie: The amount of heat required to raise the temperature of one kilo gram of water through 1⁰ C is called as one Kilo-Calorie.

Temperature: Temperature is the degree of hotness or coldness of a body. It is measured by the thermometer. The temperature is not another name of heat. Temperature of a body is a measure of its hotness which can be defined as a property determining the rate at which heat will be transferred to or from it.

Different type of temperature scales:

i)                    Celsius scale(Centigrade scale): The temperature scale originally devised by Anders Celsius in which the melting point of ice was 0⁰ C and the boiling point of water was 1000C is known as Celsius scale.

ii)                  Fahrenheit scale: The temperature scale, in which the melting point of ice is taken as 32⁰F and the boiling point of water under standard atmospheric pressure (760 mm) as 212⁰F, is known as Fahrenheit scale.

iii)                Reaumur scale: The temperature scale, in which the melting point of ice is taken as 0⁰R and the boiling point of water as 80⁰R, is known as Reaumur scale.

                                                                                                                   C     F-32       R

The relation between Celsius scale, Fahrenheit scale and Reaumur scale is ---- = ------- = ----

                                                                                                                                       5         9          4

40⁰ is the temperature same on Celsius and Fahrenheit.

Newton’s law of motion: These are fundamental laws on which classical dynamics is based.

i)                    1^st Law – Every body continues in its state of rest or uniform motion in a straight line except in so far as it is compelled by external forces to change that state.

ii)                  2^nd Law – Rate of change of momentum is proportional to the applied force and takes place in the direction in which the force acts.

Parallelogram law of forces: This law states that if two forces acting at a point are represented in magnitude and direction by two adjacent sides of a parallelogram, the resultant of the two forces is similarly represented by the diagonal of the parallelogram passing through the common point.

Triangle law of velocities: This law states that if two simultaneous velocities possessed by a particle can be represented in magnitude and direction by the two sides of a triangle taken in order, their resultant is represented in magnitude and direction by the third side taken in the reverse order.

pH Value: The logarithm, to the base 10, of the reciprocal of the concentration as the number of grams of hydrogen ions per litre of a solution is called as the pH value of the solution which is useful as a measure of the acidity of a solution and  expressed as :

                        1

pH = log₁₀ -------- where (H⁺) is the hydrogen ion concentration.

                    (H⁺)                                     1

The pH value of pure water will be log10 ------- = 7 which is taken to represent neutrality of the pH scale

                                                                           10^-7

Addition of acid causes increase in hydrogen ion concentration thus decreasing the pH value. A pH value below 7 indicates acidity and similarly a pH-value in excess of 7 indicates alkalinity.