Physical world class 11
The quantities by means of which we describe the laws of physics are called Physical Quantities.
The ‘Standared’ of measurement of a physical quantity is called the unit of that physical quantity.
The magnitude of physical quantity = NU, where
N = Numerical value of the measure of the quantity and
U = Unit of the quantity.
The Unit of length, mass and time are called fundamental units. The units of other quantities which are derived from mass, length and time are called derived units.
The system of Units: The common system of units are :
(i) FPS system: The units of length, mass and time are respectively foot, pound and second.
(ii) CGS system: The units of length, mass and time are respectively centimetre, gram and second.
(iii) MKS system: The units of length, mass and time are a respectively metre, kilogram and second.
(iv) The International system of units (SI units).
By international agreements the seven base units of the S.I. system are :
The metre (m) ———– Standard of length.
The kilogram (kg) ———— Standard of mass.
The second (s) ———— Standard of time.
The Kelvin (K) ———— Standard of temperature.
The candela (cd) ———— Standard of luminous.
The mole (mol) ———— Standard of the amount of substance.
The ampere (A) ———— Standard of electric current.
In addition to this, there are two supplementary SI Units: Supplementary Quantities are those physical quantities whose unit is assumed but having no dimension called supplementary quantities. e.g
1. Radian for the plane angle: It is 2-D angle, it occupies the length
2. Steradian for the solid angle.It is 3-D angle. It occupies the area e.g sphere ball like structure.
Ω = Surface area = Surface area/(Radius)2]rad.
Maxm value of Ω = 4πr2/r2= 4π rad. =4 × π = 4 × 180= 7200
Radian and degree are the Units of angle. = 360°.
Dimensions of a physical quantity are the powers to which the fundamental quantities must be raised to represent the given physical quantity. In mechanics, all physical quantities can be expressed in terms of mass (M), length (L) and time (T).
Example : Force = mass acceleration =
So the dimensions of force are 1 in mass, 1 in length and – 2 in time.
In the equation
if a = b = c = 0, then the quantity is called dimensionless.
Examples: Strain, specific gravity, angle. They are the ratio of two similar quantities.
Number, such as 8, 1/16, sinθ, μ etc.
A dimensionless quantity has same numeric value in all system of units.
Uses of Dimensional equation
A. To change the value of a physical quantity from one system to another :
n1 u1= n2 u2
Example: Convert 1 Newton into dyne.
Force = mass × acceleration.
In this way, the conversion factor for any derived physical quantity can be calculated if the dimensional formula of the derived quantity is known.