Units of Measurement of Physical Quantities and their Dimensions

Physics deals with the matter and energy and also deals with their inter conversions. Physics is nothing but science of measurements. Physical quantities are those quantities, which can be measured. Physical quantities will have magintudes as well as units of measurement so that they can express the exact quantity of measurement.

All the physical quantities are classified into two categories, namely fundamental physical quantities and derived physical quantities. The fundamental physical quantities cannot be expressed in terms of other physical quantities whereas derived physical quantities can be expressed in terms of fundamental quantities or other derived quantities. The examples of fundamental quantities are length, mass and time and the examples of derived quantities are area, speed, acceleration, etc.

Units of Measurement of Physical Quantities

• Units are the standards of measurement of physical quantities. The systems of measurement of physical quantities are FPS (Foot, Pound, Second), MKS (Meter, Kilogram, Second) and CGS (Centimeter, Gram, Second).
  
  
• There is another system called SI (International System of Units) system in which there are 7 fundamental quantities.

  Units of Measurement of Fundamental Physical Quantities

  The following list shows 7 fundamental physical quantities and their units of measurement:

  
  

  Fundamental Physical Quantity	Unit of Measurement (SI system)
  Length	Meter (m)
  Mass	Kilogram (kg)
  Time	Second (s)
  Electric Current	Ampere (A)
  Temperature	Kelvin (K)
  Amount of substance	Mole (mol)
  Luminous Intensity	Candela (cd)

  
  
  

  Units of Measurement of Derived Physical Quantities

  The following list shows some important derived physical quantities and their units of measurement:

  
  

  Derived Physical Quantity	Formula	Unit of Measurement (SI system)
  Area	Length x Breadth	m2
  Volume	Length x Breadth x Height	m3
  Speed	Distance/Time	m/s
  Velocity	Displacement/Time	m/s
  Acceleration	Velocity/Time	m/s2
  Density	Mass/Volume	kg/m3
  Momentum	Mass x Velocity	kg x m/s
  Force	Mass x Acceleration	kg x m/s2 (or) Newton (N)
  Pressure	Force/Area	N/m2 (or) Pascal (Pa)
  Work (and) Energy	Force x Distance	N x m (or) Joule (J)
  Power	Work/Time	J/s (or) Watt (W)
  Impulse	Force x Time	N x s
  Torque (or) Moment of Force	Force x Distance	N x m
  Surface Tension	Force/Length	N/m
  Moment of Inertia	Mass x (distance)2	kg x m2
  Current Density	Current/Area	A/m2
  Electric Charge	Current x Time	A x s

Dimensions of Physical Quantities

• The dimensions of fundamental physical quantities: Mass is M¹, Length is L¹ and Time is T¹.
  
  
• The dimension of a derived physical quantity can be termed as the powers to which the fundamental units of mass, length and time are raised to represent that derived physical quantity.
  
  The dimensions of some of the derived physical quantities: velocity is L¹ T^-1, acceleration is L¹ T^-2, momentum is M¹ L¹ T^-1 and force is M¹ L¹ T^-2.

Scalars and Vectors

• Study of objects in motion is called Mechanics. Physical quantities that depict the motion of objects are classified into two categories, scalars and vectors. Scalars are those physical quantities that have only magnitude and vectors are those physical quantities that have both magnitude and direction.
  
  Examples of scalars are Mass, Speed, Distance, etc. and examples of vectors are Displacement, Velocity, Force, etc.
  
  
• Time (t) rate of change of distance of a body is called speed. Time rate of change of displacement (s) is called velocity. Uniform motion means uniform velocity (v). Time rate of change of velocity is called acceleration (a).
  
  Velocity, v = ( s_f – s_i )/( t_f - t_i ) ( m/s ), where 'f' represents final quantity and 'i' represents initial quantity
  
  Acceleration, a = ( v_f – v_i )/( t_f – t_i ) ( m/s² )
  
  Momentum, p = mv ( kg m/s ), where m is the mass of the body.
  
  Force, F = ma ( kg m/s² or N ), where N is Newton.
  
  

1. Match the fundamental physical quantities with their respective SI units:
   
   
   1. Luminous Intensity
   
   
   2. Amount of Substance
   
   
   3. Temperature
   
   
   4. Electric Current

   
   
   

   1. Kelvin
   
   
   2. Ampere
   
   
   3. Mole
   
   
   4. Candela
   
   
   
   1. a-1, b-2, c-4, d-3
   
   
   2. a-2, b-3, c-1, d-4
   
   
   3. a-4, b-3, c-1, d-2
   
   
   4. a-3, b-4, c-1, d-2
   
   Answer
   
   Ans: C
   
   
   
2. What is the SI unit of Pressure?
   
   
   1. Newton
   
   
   2. Joule
   
   
   3. Watt
   
   
   4. Pascal
   
   Answer
   
   Ans: D