Presentation on Units and dimensions

1. Chapter- 1

2.  What is Physics ?
Physics, the study of matter and energy, is an ancient and broad field of
Science. The word 'physics' comes from the Greek 'knowledge of nature,'
and in general, the field aims to analyze and understand the natural
phenomena of the universe. It's often considered to be the most
fundamental science. It provides a basis for all other sciences - without
physics, you couldn't have biology, chemistry, or anything else!
Mathematics is the language of Physics. Without knowledge of
Mathematics it would be much more difficult to discover, understand, and
explain laws of nature.
Units - All physical quantities are measured w.r.t. standard magnitude of
the same physical quantity and these standards are called UNITS. eg.
second, meter, kilogram, etc. So the four basic properties of units are:—
1. They must be well defined.
2. 2. They should be easily available and reproducible.
3. 3. They should be invariable e.g. step as a unit of length is not invariable.
4. 4. They should be accepted to all.
e.g. if some body has to study 4 hrs, the numeric part 4 says that it is 4 times
of the unit of time. The second part says that the unit chosen for time is
hour.

3.  SET OF FUNDAMENTAL QUANTITIES
A set of physical quantities which are completely independent
of each other .
Physical quantities is called Set of Fundamental Quantities.
Physical Quantity Units(SI) Units(CGS) Notations
Mass kg(kilogram) g M
Length m (meter) cm L
Time s (second) s T
Temperature K (kelvin) °C Theta
Current A (ampere) A I or A
Luminous intensity cd (candela) — cd
Amount of substance mol — mol

4.  Physical Quantity Definition
(SI Unit)
Length (m) The distance travelled by light in vacuum in
1/299,792,458 second is called 1 metre.
Mass (kg) The mass of a cylinder made of platinum-
iridium alloy kept at International Bureau of
Weights and Measures is defined as 1 kilogram.
Time(s) The second is the duration of 9,192,631,770 periods
of the radiation corresponding to the transition
between the two hyperfine levels of the ground
state of the cesium- 133 atom.
Electric Current (A) If equal currents are maintained in the two parallel
infinitely long wires of negligible cross-section, so
that the force between them is 2 × 10–7 Newton per
metre of the wires, the current in any of the wires is
called 1 Ampere.

5.  Physical Quantity Definition
(SI Unit)
Thermodynamic The fraction 273.16 1 of the thermodynamic
Temperature (K) temperature of triple point of water is called 1
Kelvin
Luminous Intensity(cd) 1 candela is the luminous intensity of a black
body of surface area 1/600,000 m2 1 placed at
the temperature of freezing platinum and at a
pressure of 101,325 N/m2 , in the direction
perpendicular to its surface.
Amount of substance (mole) The mole is the amount of a substance that
contains as many elementary entities as there
are number of atoms in 0.012 kg of carbon-12

6.  There are two supplementary units too:
 1. Plane angle (radian) angle = arc / radius
Theta= l / r
 2. Solid Angle (steradian)
System of Units : The common system of units are :
1.FPS system : The units of length, mass and time are respectively foot, pound and
second.
2.CGS system : The units of length, mass and time are respectively centimeter, gram
and second.
3.MKS system : The units of length, mass and time are respectively metre, kilogram
and second.
4.The International system of units (SI units).

7. Derived Quantities
The Physical quantities that depend upon other physical quantity for its
measurement are known as derived quantities. The measurement of derived
quantities directly depends upon other quantities. So in order to measure the derive
quantity, one must measure the quantities that it depends upon. Except 7
fundamental quantities, all other quantities are derived quantities. Some examples
of derived quantities are:
 Derived Units
 Volume l (or lit) 0.001 m3 1000 cm3
 Force Newton (SI)N1 kg · m/s2 Dyne (CGS) 1 g ·cm/s2
 Pressure Pascal (SI)Pa1 N/m2
 Energy, work Joule (SI)J 1 N · m = 1 kg · m2/s2
 Erg (CGS) 1 dyne · cm = 1 g · cm2/s2
 Gram-calorie cal 4.184 J = 4.184 kg · m2/s2
 PowerWatt W1 J/s = 1 kg · m2/s2

8. Dimensions
 Dimensions of a physical quantity are the powers to which the fundamental quantities
must be raised to represent the given physical quantity. In mechanics all physical
quantities can be expressed in terms of mass (M), length (L) and time (T).
 Example : Force = mass x acceleration = Or,
 So, the dimensions of force are 1 in mass, 1 in length and – 2 in time
Dimensionless quantity
In the equation
then the quantity is called dimensionless.
Examples : Strain, specific gravity, angle. They are ratio of two similar quantities.
A dimensionless quantity has same numeric value in all system of units

10. Uses of Dimension
 Dimensional consistency of of any equation with physical sense must be
identical. Otherwise, an equality in one system would be broken upon
conversion to another system.
 This fact is used to obtain derived units from fundamental units.
Example
 In the LMT class, the dimension of mass is M, the dimension of
acceleration is LT−2, the
Dimension of force can be obtained (derived) from Newton’s second law:
f = ma
[f] = [m] [a] = MLT−2
 In other words, in the LMT class, the dimension of force is LMT−2.
We can determine the unknown exponent “?” in the following equation
by requiring the same units on both sides:
E = mc?
ML2T−2 = M(LT−1)?
? = 2
 This is one technique of Dimensional Analysis, which can allow us to
identify the controlling physical quantities in unfamiliar or complicated
quantities.

11. Limitations in Dimensional Analysis
 Dimensional method can not be used to derive equation
involving addition or subtraction.
 In some cases, it is difficult to guess the factors while
deriving the relation connecting two or more physical
quantities.
 Equations using trigonometric, exponential or logarithmic
expression can not be deduced.
 If dimensions are given , physical quantity may not be
unique as many physical quantities having same
dimensions.
For example dimensional formula of a physical quantity is
ML2T-2, it may be work or energy or torque.

12. Limitations in Dimensional Analysis
 It cannot be used if the physical quantity is dependent
on more than three unknown variables.
 This method cannot be used in an equation containing
two or more variables with same dimensions.
Equation of frequency of a tuning fork f=(d/L2)v can
not be derived by theory of dimension but can be
checked.
 By Jai Sharma of class 11th science A