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I have a test coming up in a few days and I'm not the best at physics, so I thought I'd make a few pointers
units
when measuring any physical quantity we compare it to a standard reference point known as a unit |
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i) fundamental units, these are fundamental or base quantities which are not derived |
ii) derived units, these are the units of other physical quantities and can be expressed as a combination of multiple fundamental units |
(together they are know as the system of units) |
international system of units
CGS system- the system where centimeter (L), gram (M), seconds (T) |
FPS system [british system]- the system where foot (L), pound (M), seconds (T) |
MKS system- the system where meter (L), kilogram (M), seconds (T) |
International system of units
SI units- it's the present system of units which is internationally accepted for measurement. |
It has seven base units which then can be combined with each other to form the derived units |
SI units
quantity |
name |
symbol |
length |
meter |
m |
mass |
kilogram |
kg |
time |
second |
s |
electric |
ampere |
A |
Thermodynamic temperature |
kelvin |
K |
Amount of substance |
mole |
mol |
Luminous intensity |
candela |
cd |
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Dimensions of Physical quantities
the dimensions of a physical quantity are the powers (or the exponents) to which the base quantities are raised to represent that quantity |
square brackets [ ] are used to indicate the dimensions |
An equation obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the physical quantity. In other words it can be said that dimensional equations represent the dimensions of a physical quantity in terms of the base quantity |
examples
Volume - [V] = [M0 L3 T0] |
Speed - [v] = [M0 L T-1] |
Force - [F] = [M L T-2] |
Mass density - [p] = [M L-3 T0] |
dimensional analysis
Dimensional analysis is the practice of checking relations between physical quantities by identifying the dimensions of the physical quantities. These dimensions are independent of the numerical multiples and constants |
It helps us deduce certain relations between different physical quantities and checking the derivation, accuracy and dimensional consistency of the mathematical expressions |
applications of dimensional analysis
We make use of dimensional analysis for three prominent reasons: |
1) To check the consistency of a dimensional equation |
2) To derive the relation between physical quantities in physical phenomena |
3) To change units from one system to another |
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limitations of dimensional analysis
Some limitations of dimensional analysis are:
1) It doesn’t give information about the dimensional constant.
2) The formula containing trigonometric function, exponential functions, logarithmic function, etc. cannot be derived.
3) It gives no information about whether a physical quantity is a scalar or vector. |
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