What are Units.

In my previous post, I explained with examples how to solve the problems in physics.

To solve problems and to under stand the basics of the Physics it is very important to know what is a physical quantity, types of physical quantities.What is a unit, what are the units of different physical quantities, types of units, symbols of units.

There is"one and only one" branch of science which measures a physical quantity, that branch of science is “Physics”. Measurements have an important role not only in physics, but also in every branch of science and everywhere in our day-to-day life.

To measure physical quantities we need units. Let’s try to understand necessity of measurements and "units of measurements" in Physics.

The information about a physical quantity, by description of its external properties like color, taste etc is incomplete with out knowing its temperature, size (dimensions), which depends on measurement, i.e. with out measurements it is impossible to know completely about the external properties of any object. So, it becomes necessary to measure it.

As we know, to measure a physical quantity we require a unit. Different physical quantities will have different units.

What is unit? A standard reference of the same physical quantity is essential to measure any physical quantity. That standard which we use to measure a physical quantity is called unit.

Let me put it this way, if we want to measure length of a table, we have to select a standard length (length of our hand), and by comparing the table’s length with the standard length we can measure the length of the table. If the table is 3.5 times that of standard length, i.e. length of our hand then we can write the result as “length of table = 3.5 times the length of our hand or 3.5 units. In this example length of hand is taken as standard length or unit to measure the table’s length.

Like that we can define any convenient standard or unit to measure a physical quantity.

But, if we choose a standard as in the above example which is not consistent, can not be reproduced. Because of such undefined units, errors and confusion in measurements will creep in. To avoid such confusion, instead of taking any undefined reference as a standard, well-defined and universal standards are used. Such a well-defined reference taken a standard is generally called a well defined unit or unit.

Measurement of every physical quantity will have two parts, a number (n) followed by a unit (u).
There fore n u = constant.

Ex: If the length of a table is 1.2 meters.In this measurement number n= 1.2 and unit is meter.

→ length (L)=n₁u₁ = 1.2 meters
→ length (L)=n₂u₂ = 120 centimeters
→ length (L)=n₃u₃= 1200 millimeters
From the above data we can understand that

i) we can measure a physical quantity in different units.what ever may be the unit it’s value is same.
→ L = n₁u₁= n₂u₂ = n₃u₃
ii) If the unit chosen smaller ,the multiple number will be greater.
→ u₁>u₁>u₁ ==> n₁<n₂<n₃
nu = constant ==> n₁u₁=n₂u₂ or u proportional to 1/n
or n proportional to 1/u

==>n1 /n2 = u2/ u1

Generally we can use any convenient unit to measure a physical quantity depending on how much magnitude we are measuring or in which system of units we want to measure it.

What kind of unit we should use?
The unit i) must be accepted internationally.ii) Should be reproducible.iii) Should be invariable.iv) Should be easily available.v) Should be consistent.vi) Should be large, if the physical quantity to be measured is a big quantity.

Ex: To measure larger lengths we use units like Km, mt etc, to measure large magnitude of time
we use units like hour , day ,week, month , year etc.

vii) Should be small if the physical quantity to be measured is small.
Ex: To measure small magnitude time, we use units like millisecond, microsecond etc
To measure small lengths we use units like millimeter, centimeter etc.
Types of physical Quantities.:
We can broadly divide the physical quantities in to two types i)Fundamental Physical quantities ii)Derived physical quantities.

Fundamental physical quantities: A physical quantity which can exist independently is called Fundamental physical quantity.
Ex: Length, mass and time etc.
Derived physical quantities: A physical quantity which can not exist independently is called derived physical quantity. (Or) A physical quantity which is dependent or derived from any other physical quantity is called derived physical quantity.
Ex : Area, volume, density, speed, acceleration, force, energy etc.

Like the physical quantities, we can Divide the units in to two types.
i)Fundamental units ii)derived units.

Fundamental units : The units of fundamental physical quantities are called fundamental units, (or) The units which are independent or can not derived from any other unit is called fundamental unit.

Ex:­Every unit of length is fundamental unit (irrespective of the system to which it belongs); millimeter, centimeter, meter, kilometer etc.
­Every unit of time is a fundamental physical quantity ; microsecond, millisecond, second, minute, hour, day etc.

Derived units: The units of derived physical quantities are called derived units. Ex: Units of area, volume, speed, density, energy etc are derived units.
Ex: ­ Every unit of speed is a derived unit ; m/sec, cm/sec, km/hr etc.
­Every unit of density is a derived unit; kg/m³, gr/cm³ etc.
­Every unit of acceleration is a derived unit; m/sec², cm/sec², km/hr² etc.

Systems of units: To measure the fundamental physical quantities Length, Mass and time we have three systems of units, they are i) C.G.S System (Metric system) ii)F.P.S System (British system) and iii)M.K.S System. In all these three systems only three physical quantities length, mass and time are considered to be fundamental quantities.

But, in systems Internationale (S.I) system there are seven fundamental physical quantities. Which are i)Length ii)Mass iii)Time iv)Electric current v) Thermodynamic temperature vi)Luminous intensity vii)Quantity of substance.

In addition to these two more quantities were added as supplementary physical quantities. They are i)Plane angle ii)Solid angle.

Systems,Fundamental physical quantities and their units:In
C.G.S system: Length (centimeter); Mass (gram); Time (second).

F.P.S system :Length (foot);Mass(pound);Time (second).

C.G.S system: Length (meter); Mass (kilogram); Time (second).

S.I System:Length (meter); Mass (kilogram); Time (second); Electric current (ampere); Thermodynamic temperature (kelvin); Intensity of light (candela); Quantity of matter (mole). The units of suplimentary quantities are Plane angle( radian); Solid angle(Steradian).