Scalars and Vectors- PHYSICS AND ITS ELEMENTS

Scalars:

 The physical quantities that are completely characterized by magnitude is called scalars, e.g.    distance, speed, work, energy, power, temperature, current, large angles, all potential, all fluxes etc.

Vectors:

The physical quantities having both magnitude and direction are called vectors. e.g. Displacement, force, momentum, potential gradient, magnetic induction, electric dipole moment, small angles elementary area, all fields and field intensities, all gradients etc.

Tensor:

A quantity whose magnitude differs from direction to direction eg: pressure, stress, moment of inertia, modulus of elasticity, coefficient of viscosity etc.

1. Current has both magnitude and direction however; it is not a vector quantity because it does not follow the law of vector addition.
2. The necessary condition for a physical quantity to be a vector is that it should have direction while the sufficient condition is that it should follow the low of vector addition.
3. A vector quantity with zero magnitude is called a null vector.
4. A vector quantity with unit magnitude is called unit vector.

Units,Dimensions,Conversion and Significant digits in physics

Measurement:

The method of comparing any amount of a physical quantity with standard amount of same kind is called measurement. Measurement of a physical quantity consists of a numerical value (n) and a unit(u)

Therefore,

Measurement=Numerical Value(n)*Unit(u)

Unit:

There are 3 kinds of unit.

a) Fundamental unit :

    The units of fundamental quantities that cann't be derived from other units.

    Example:kg,meter,second etc.

    It is 7 in number.

b)Supplementary units:

    Example: Units of plane angle and solid angle.

c) Derived units:

    The units derived from fundamental and supplementary units.

    Example: Joule, Pascal, Newton etc.

 Systems of Units:

 There are four system of units.

 a) CGS System: In this system units for length , mass and time are centimeter(m),gram(m) and              seconds(s) respectively.

 b) FPS System: Units for length ,mass and time are Foot(ft), pound(lb) and second(s) respectively.

 c) MKS System: Units for length for length, mass and time are meter(m), Kilogram(kg) and                    second(s) respectively.

 d) SI System: In this system, there are seven fundamental quantities and fundamental units.

Fundamental Units (In SI System):

Physical Quantity	Units	Symbol
Length mass time temperature luminosity electric current amount of substance	Meter kilogram second kelvin candela ampere mole	M kg s k cd a mol

Supplementary Units:

Physical Quantity	Units	Symbol
Plane angle Solid angle	Radian steradian	r sr

Conversion Factor:

1litre       = 10^-3 m³

1 g/cm³    = 10³ kg/ m³
1 N           = 10⁵ dyne
1 atm       = 1.01*10⁵ N/M²
1hp           = 746w
1cal          = 4.2J
1Kwh        = 3.6*10⁶ J

Dimensions and Dimensional Formulae:

·         The dimensions of a derived unit may be defined as the powers to which the fundamental units of mass, length and time must be raised to represent it.

For example:

Velocity=displacement/time

·         Thus the dimensions of the unit of velocity are one in length and -1 in time. Its dimension in mass is zero.

·         Work, energy ,quantity of heat , quantity of light, internal energy, torque each has dimensional formula ML²T^-2 (kgm²/s²)

·         Velocity, Speed, distance covered in nth second have same dimensional formula m⁰LT^-1 (M/S).

·         Pure numbers are dimensions.

Dimensions of Some Physical Quantities:

S.N	Physical Quantity	Dimensions	SI units
1	Density (D=M/V)	[ML-3]	Kg m-3
2	Force (F=Ma)	[MLT-2]	Kgms-2
3	Linear momentum (P=MV)	[MLT-1]	Kgms-1
4	Work or Energy(W=F*D)	[ML2T-2]	Kgm2s-2
5	Power (P=w/t)	[ML2T-3]	Kgm2s-3
6	Pressure (P=F/A)	[ML-1T-2]	Kgm-1s-2(N/M2)
7	Impulse(=F*t)	[MLT-1]	Kgms-1
8	Strain	[M0L0T0]	No Unit
9	Frequency (f)	[T1]	Hz
10	Stress (F/A)	[ML-1T2]	Kgm-1s-2