Measurements

1
Chapter-1

• Measurements

2
Ch 1-2 Measuring Things

• Discovery of Physics Through measuring Physical
  Quantities such as length, time, mass,
  temperature, pressure and electric current
• Units and Standards.
• Measurements of Physical quantity in its own
  Unit by comparison with a Standard.
• Each physical quantity has its own unit and each
  unit has its own standard
• Two groups of Quantities Base and Derived
• Base Physical Quantities
• Length (L) , Mass (M) and Time (T)
• Derived Physical Quantities (Ratio or Product of
  two Base Units)
• speed length/time
• acceleration speed/time
• force mass x acceleration

3
Ch 1-2 Measuring Things

• Two Groups of Units
• Base Units Length, Time, Mass
• Derived Units length/time mass x velocity
• Base-Standards associated with base Units
• Derived-Standard associated with derived Units
• Base Unit System
• International System (mks)
• Gaussian System (cgs)
• British engineering system (fps)

4
Table of Base Units
5
Prefix for SI units
Prefix Prefix are used to increase or decrease
SI units
6
Ch 1-4 Changing Units-Chain-link conversion

• Changing units using Chain-link conversion
• Multiplication of original measurement by a
  conversion factor c
• ratio of units ( new unit/old unit)
• Change of 5 min into seconds
• conversion 1 min60 s or 1 min/60 s 1
• 60 s 1min or 60 s/ 1min 1
• Conversion factor c 60 s/1 min
• 5 min 5 min x c 5 min x (60 s/1 min)300 s
• Conversion factor f for changing year into
  seconds
• f (365 days/1year)x(24 h/1day) x (60 min/ 1 h)
  x (60 s/1 min)

7
Significant Figures

• Precession in data given by Significant Figures
• Significant Figures (SF) number of digits in
  a number,
• 33 m/s has two digits hence two SF
• 1.33 m has three SF
• Final Result of a calculation cannot be more
  precise than the least significant figure in the
  data
• Z A(2 SF) x B(3 SF)
• Z will be rounded off to have 2SF number
• 3.15 or 3.15 x103 has 3SF
• 3000 has 4SF or
• 3 x103 has 1SF or
• 3.0 x103 has 2SF or
• 3.00 x103 has 3SF or
• 3.000 x103 has 4SF or

8
Ch 1-5 Standard of Length

• SI Standard of length-meter
• Length of a platinum-iridium bar (standard
  meter bar) kept at International Bureau of
  Weights and Measures near Paris
• SI Standard of length using speed of light
• c 299792458 m/s
• The meter is the length of the path traveled by
  light in a vacuum during a time interval of
  1/299792458 of a second

9
Ch 1-6 SI Standard of Time

• SI Standard of time-second
• Any phenomenon that repeats itself is a possible
  time standard
• Time measurement with reference to frequency
  (f9,192,631,770 Hz) of light emitted by
  cesium-133 atom (atomic clock)
• One second is the time taken by 9,192, 631,770
  oscillations of light emitted by a cesium-133 atom

10
Ch 1-7 SI Standard of Mass

• SI Standard of mass-kilogram
• Mass of a platinum-iridium cylinder ( The
  Standard kilogram) kept at International Bureau
  of Weights and Measures near Paris.
• Second Mass Standard
• Atomic mass unit (amu)
• 1 amu 1.6605402 x 10-27 kg

11
Dimensional Analysis

• Dimension denotes qualitative nature of a
  physical quantity
• Symbols L, M, T are used to specify length, mass
  and time nature of a physical quantity
  respectively.
• The brackets are used to denote the
  dimension of a physical quantity velocity v and
  area A
• v L / T A L2
• Dimensions are treated as algebraic quantities
  and can be multiplied or divided mutually

12
Dimensional Analysis

• Dimensional Analysis is used to check a formula
• A formula is correct only if the dimension of
  both side of the relationship are same.
• Example Acceleration of a particle moving in a
  circle is given by akrnvm
• Determine the values of constant k and exponents
  n and m
• The dimensional equation is L/T2Ln(L/T)mLnm/Tm
• Equating exponents of L and T separately
• 1nm 2m m2 n1-m1-2-1
• Then L/T2 k L/T2 and k1
• Hence akrnvm r-1v2 v2/r