CHAPTER-1

Measurements

Chapter 1- Measurement

Topics to be covered :

Measurement of a physical parameter

Units, systems of unitsBasic units in mechanicsChanging unitsSignificant figures

Ch 1-2 Measuring Things Units and Standards. Measurements of Physical quantity

in unit in comparison with a standard.

Each Physical Quantities has its associated unit and a standard to compare with

Base Physical Quantities : Length (L) , Mass (M) and Time (T) Derived Physical Quantities: speed = length/time acceleration = speed/time force = mass x acceleration

Ch 1-2 Measuring Things

Base Unit associated with base quantities

Derived Units associated with derived quantities

Base-Standards associated with base physical quantities

Derived-Standards associated with derived quantities

Base Unit Systems International System (mks) Gaussian System (cgs) British engineering system (fps)

Table of Base Units System

System Length Mass Time

SI(mks) meter (m) kilogram(kg)

second(s)

Gaussian (cgs) centimeter(cm)

gram (g) second(s)

British (fps) foot (ft) slug*pound

second(s)

Prefix

A multiplier of a unit to increase or decrease its value

Prefix in SI units given in terms of power of tens

Prefix for SI units

Factor Prefix Symbol

1012 tera T

109 giga G

106 mega M

103 kilo k

10-2 centi c

10-3 milli m

10-6 micro 10-9 nano n

10-12 pico p

Ch 1-4 Changing Units

Changing units using Chain-link conversion

Multiplication of original measurement by a conversion factor c

Change of 5 min into seconds Conversion factor c = 60 s/1 min 5 min= 5 min x c = 5 min x (60 s/1

min)=300 s Conversion factor c for changing

year into seconds c =(365 days/1year)x(24 h/1day) x (60 min/ 1 h) x (60 s/1 min)

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

Standards -SI units system

SI (mks) Unit System

Length Mass Time

meter (m) kilogram (kg) second (s)

The Meter A

C

B

Earth

Equator

In 1792 the meter was defined to be one ten-millionth of the distance from the north pole to the equator.

The meter was later defined as the distance between two fine lines on a standard meter bar made of platinum-iridium.

Since 1983 the meter is defined as the length traveled by light in vacuum during the time interval of 1/299792458 of a second.

The measurement of the speed of light had become extremely precise.

71 m

10

AB

Ch 1-5 Length

SI unit of length-meter Length of a platinum-iridium bar

(standard meter bar) kept at International Bureau of Weights and Measures near Paris

The meter is the length of the path traveled by light in a vacuum during a time interval of 1/299792458 of a second:

speed of light c =299 792 458 m/s

The SecondInitially the second was defined as follows:

The length of the day is not constant as is shown in the figure.

Since 1967 the second is defined as the time taken by 9192631770 light oscillations of a particular wavelength emitted by a cesium-133 atom.

it would take two cesium clocks 6000 years before their readings would differ by more than 1 second.

11 second

24 60 60of the time it takes the Earth

to complete a full rotation

about its axis.

Ch 1-6 Time

SI unit of time-secondTime measurement with

reference to frequency (9 192 631 770 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

The Kilogram

The SI standard of mass is a platinum-iridium cylinder shown in the figure. The cylinder is kept at the International Bureau of Weights and Measures near Paris and assigned a mass of 1 kilogram. Accurate copies have been sent to other countries.

Ch 1-7 Mass

SI unit 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 Mass of C-12 atom = 12

amu

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] = L / T ; [Area A] = L2

Dimensions are treated as algebraic quantities and can be multiplied or divided mutually

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 : a=krnvm

Determine the values of constant k and exponents n and m

The dimensional equation is L/T2=Ln(L/T)m=Ln+m/Tm

Equating exponents of L and T separately:

1=n+m; 2=m; m=2; n=1-m=1-2=-1 Then L/T2 = k L/T2 ; and k=1

Hence a=krnvm = r-1v2 = v2/r

Thank you