Dimension & Measurements
A). Fundamental, Absolute or Base Quantities
(1) length
(2) mass
(3) time
(4) electric current,
(5) thermodynamic temperature
(6) amount of substance
(7) luminous intensity.
B). Derived quantities
Physical quantities which can be expressed in terms of base quantities are called as derived quantities. :
Ex: Speed, velocity, acceleration, force, momentum, pressure, energy etc
C). Supplementary Quantities
Beside the seven fundamental physical quantities two supplementary quantities are also defined :
(1) Plane angle (2) Solid angle.
NOTE: Supplementary quantities have only units but no dimensions.
Magnitude
Magnitude of physical quantity = (numerical value)
unit
Measurement of any physical quantity is expressed in terms of an internationally accepted certain basic reference standard called unit
Principle systems of Unit
Supplementary units
(1) Plane angle : radian (rad)
(2) Solid angle : steradian (sr)
Definitions of important SI Units
Meter :
1 m = 1,650, 763.73 wavelengths in vaccum, of radiation corresponding to organ-red light of krypton-86
Second
1 s = 9,192, 631,770 time periods of a particular from Ceasium – 133 atom
Kilogram :
1kg = mass of 1 liter volume of water at 4°C
Kelvin
1 K = 1/273.16 part of the thermodynamic temperature of triple point of water
Mole :
It is the amount of substance of a system which contains as many elementary particles as there are atoms in 12g of carbon – 12
Ampere
It is current which flows through two infinitely long straight conductors of negligible cross-section placed at a distance of one meter in vacuum produces a force of 2 × 10^–7 N/m between them
Candela
It is luminous intensity in a perpendicular direction of a surface of 1/600000 m2 of a black body at the temperature of
freezing point under a pressure of 1.013 × 10^5 N/m2.
Radian
It is the plane angle between two radiia of a circle which cut-off on the circumference, an arc equal in length to the radius
Steradian
The steradian is the solid angle which having its vertex at the center of the sphere, cut-off an area of the surface of sphere equal to that of a square with sides of length equal to the radius of the sphere.
SI PreFix
Some special types of units
- 1 Micron (1u) = 10^–6 m (length)
- 1 Angstrom (1 Å) = 10^–10m (length)
- 1 fermi (1f) = 10^–15 m (length)
- 1 inch = 2.54 cm (length)
- 1 mile = 1.609 km (length)= 5280 feet
- 1 atmosphere = 10^5 N/m2 =76 mm of Hg= 76 torr (pressure)
- 1 liter = 10^–3 m^3 = 1000 cm^3 (volume)
- 1 carat = 0.0002 kg (weight)
- 1 pound (Ib) = 0.4536 kg (weight)
Some important Units and their Dimensions
Scalar and Vector
Limitations of Dimensional Analysis
(i) Value of dimensionless constant can not be calculated.
(ii) Equation containing trigonometrical, exponential and logarithmic terms cannot be analyzed.
(iii) If a physical quantity depends on more than three factors, then relation among them cannot be
established
SCALAR QUANTITY OR SCALAR
A physical quantity that has magnitude only is called scalar quantity.
Example : speed, distance, Volume, mass, pressure, electric current, surface tension etc
VECTOR QUANTITY OR VECTOR
A physical quantity has magnitude and direction and must obey law of vector addition is called
vector quantity
Example : force, torque, angular momentum, momentum, displacement, velocity, angular velocity, impulse etc.
Surface tension is a scalar quantity?
It is represented by direction, even though it is not a vector quantity. Any quantity which has
unified direction is treated as scalar. Surface tension always directs along the tangent of the surface of
the liquid, therefore it is a scalar quantity.
- Scalar quantity may be negative. e.g. charge, electric current, potential energy, work etc.
- Scalar quantity may have direction. e.g., pressure, electric current, surface tension etc.
- Small element of length dl , small element of surface dA and small angular displacement are treated as vectors.
Equation of Motion
