Scalars and vectors GSEB/CBSE/JEE/NEET

If Minimum two coordinates are required to describe motion of a particle, this motion is called two dimensional motion or motion in a plane.

1.   Scalars and vectors

      

·        In physics, we can classify quantities as scalars or vectors.

·        Basically, the difference is that a direction is associated with a vector (M+D) but not with a scalar. A scalar quantity is a quantity with magnitude only.

·        Example: Vector  Displacement, Velocity, acceleration, force, momentum, impulse, etc.

                          Scalar  Length, mass, time, volume, temperature, speed, work, energy,… etc.

  

No.	Scalar	Vector
1.	It has magnitude only.	It has magnitude as well as direction. (M+D)
2.	They change if their magnitude changes.	They change if their magnitude, direction or both changes.
3.	Scalars can be added or subtracted according to the rules of algebra.	Vector are added or subtracted by geometrical (graphical) method or vector algebra.
4.	It has no proper symbol.	It is represented by symbol  arrow.
5.	The division of a scalar by another scalar is valid.	The division of a vector by another vector is not valid.
6.	Scalar  Length, mass, time, volume, temperature, speed,	Example: Vector  Displacement, Velocity, acceleration, force,

·        Symbolically a vector is represented by a single latter with an arrow , such as force . The magnitude (value) of the vector  is denoted as   or F.

·             

      

MEASUREMENT AND SYSTEM OF UNIT (માપન તથા એકમ પદ્ધતિ ) DPP

MEASUREMENT AND SYSTEM OF UNIT (English) GSEB/CBSE

1.   UNIT: The standard measure of any quantity is called unit of that physical quantity.

              

2.   Fundamental quantities : The physical quantities which do not depend on any other physical quantity for their measurements i.e., they can be directly measured are called fundamental quantities.

Fundamental units :  The units used to measure fundamental quantities are called fundamental units.

            Examples: mass, length, time

3.   Derived quantities: Physical quantities other than fundamental quantities which depend on one or more fundamental quantities for their measurements are called derived quantities.

Examples:   ,   acceleration, momentum, force, etc.

Derived units : The units of derived quantities which depend on fundamental units for their measurements are called derived units.

Examples:   

4.   Classification of unit system

1.      British system (FPS system) → foot – pound – second system

2.      CGS system → centimetre – gram – second system

3.      MKS system → metre – kilogram – second system

4.      MKSA system → metre – kilogram – second – ampere  system

5.      SI system →  system of international (seven base units)

SI system – SI unites and their symbol

5.   The rules for writing the S.I. units  of physical quantities

a.      Unit of every physical quantity should be represented according to its symbol.             For example : m for meter not M for meter, N for newton not n for newton,

b.      Full stop and any other mark should not be written after the symbol.

For example :  kg and not kg. Or k.g. , N and not N.

c.      Symbols for units do not take plural form.

For example m is used to denote many metres also.   

d.      The units of physical quantities in numerator and denominator should be written as one ratio only.

For example the SI unit of acceleration should be written either as m/s² or m s^-2; but not as m/s/s.

e.      Full name of a unit, when it is named after a scientist, is not written with a capital letter, but the symbol for that unit has a capital letter. For example, the unit of force should be written as newton but in symbol it is written as N. The unit of pressure is Pascal in symbol it is written as Pa.