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it covers: Physical quantities (scalars & vectors). Units → fundamental & derived; systems (CGS, FPS, MKS, SI). Special units → AU, light year, parsec, angstrom, fermi. Significant figures & their rules. Dimensions & dimensional analysis (applications + limitations). Unit conversion & checking correctness of equations using homogeneity

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Units And Measurements




physical quantities

A physical quantity is a measurable property of a physical system that can be
expressed quantitatively, typically with a number and a unit. Physical quantities
can be classified into two types: scalars and vectors. Scalars are quantities that
have only magnitude, such as mass, temperature, and energy. Vectors are
quantities that have both magnitude and direction, such as velocity, force, and
acceleration.

unit
A unit is a standard quantity or measure that is used to represent or
describe a particular physical quantity or property. Units are used to
specify the magnitude or size of something, and they enable us to
make comparisons and communicate information in a standardized
and consistent way.
For example, units of length could be meters or feet, units of time
could be seconds or minutes, units of weight could be kilograms or
pounds, and units of temperature could be Celsius or Fahrenheit.



fundamental and derived units

Fundamental units
Fundamental units, also known as base units, are the basic units of measurement
for fundamental physical quantities. They are defined in terms of physical
standards, and all other units are derived from them.

, International system of units
cgs : centimeter ,gram and second.
FPS : foot, pound and second.
MKS : metre, kilogram and second.
The use of the SI is encouraged by international treaty, and it is
widely used in scientific and technical fields, as well as in
everyday life.

Derived unit
Derived units are units of measurement that are derived from
fundamental units using mathematical equations.

For example, the unit of speed is meters per second (m/s), which
is derived from the fundamental units of length and time. The unit
of force is Newton (N), which is derived from the fundamental units
of mass, length, and time.

There are many other derived units, such as joules (J) for energy,
watts (W) for power, and pascals (Pa) for pressure.


Some important units

Astronomical unit (AU)

it is a unit of measurement equal to the average
distance between the Earth and the Sun.
11
1 AU = 1.5x10 m

Light year :
A light year is a unit of distance used in astronomy that
represents the distance that light travels in one year.
15
1LY = 9.46x10 m

Arc Length
Arc Length is given by:-
d𝑠=d𝜃(𝑟)

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