Unit 1 Measurement and Uncertainties
Physics
1. The study of nature and natural phenomenon is called physics.
Need of measurement
1. Measurement is required for the precise description of a natural phenomenon.
2. It is also required to form relations between two or more pq’s.
3. It is required to formulate laws in physics.
Measurement
1. To measure any physical quantity, first we need to decide a unit for it and then
compare it with its unit.
2. For example we are to measure some length. We decided 1m as unit of length
and after comparing the given length with the unit we found that it is twice of
its unit so we write it as follows;
𝐿 = 4 × 1m = 4 m
P= MU
Unit
1. It is a specific measure or standard of a physical quantity.
Magnitude
1. It is a pure no which tells us that how many times of a unit is contained in the
given physical quantity.
Who decides the units worldwide?
1. There are three French organizations which decide the units worldwide.
a) International Bureau of Weights and Measures (BIPM)
b) General Conference on Weights and Measures (CGPM)
c) International Committee for Weights and Measures (CIPM)
Fundamental and derived units
1. Although the number of physical quantities which we measure is very large,
yet we do not need a large number of units. This is possible because the various
physical quantities are related to each other and so their units can be expressed
in terms of few basic or fundamental units.
Length, mass and time are treated as three base quantities in
mechanics. They have their independent units of measurement.
2. Base or Fundamental units: - The physical units which can neither be derived
from one another, nor they can be further resolved into simpler units are called
fundamental units.
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3. Derived units: - All the other physical units which can be expressed in terms of
the base units are called derived units. E.g.
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑆𝑝𝑒𝑒𝑑 =
= 𝑚/𝑠
𝑡𝑖𝑚𝑒
𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑡𝑖𝑚𝑒
=
𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡/𝑡𝑖𝑚𝑒
𝑡𝑖𝑚𝑒
𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
=
𝑡𝑖𝑚𝑒 2
= 𝑚/𝑠 2
𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝐹𝑜𝑟𝑐𝑒 = 𝑚𝑎𝑠𝑠 × 𝑎𝑐𝑐𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑚𝑎𝑠𝑠 ×
𝑡𝑖𝑚𝑒 2
= 𝑘𝑔 𝑚/𝑠 2
https://www.youtube.com/watch?v=Rmy85_EwL0Y
System of units
1. A complete set of both the base and derived units is called a system of units.
2. In earlier time scientists of different countries were using different system of
units for measurement. Three such systems the CGS, the FPS system and the
MKS system were in use extensively till recently.
3. International System of units (SI): - This is an internationally accepted system
of units and is basically a modification over the MKS system and is therefore
called rationalized (modified) MKS system. In this system we can obtain the
units of all the physical quantities in Physics. Because this system of units
includes four more base quantities plus two supplementary quantities. These
are as follows;
Extra base quantities
(i) Temperature (Kelvin-K)
(ii) Electric current (ampere-A)
(iii) Luminous intensity (candela-cd)
(iv) Amount of substance (mole-mol).
Supplementary quantities
(i) Plane angle (radian-rad): – The other units of plane angle are degree,
minutes and seconds.
Note: - This third category of units has been removed and now rad and sr
both are derived units now.
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Conventions for writing the units and their symbols
1. Units are always written in normal or Roman (upright) font whereas symbols
are all written in italic (slopping) fonts e.g. m represents the quantity mass
whereas m represents the unit meter.
2. The unit names are never capitalized. However, the unit symbols are capitalized
only if the symbol for a unit is derived from a proper name of a scientist e.g. m
for unit meter, N for newton, J for joule and Hz for hertz. The single exception
is L for litre. This exception is made to avoid confusion for the lower case letter
l and Arabic numeral 1.
3. Prefix symbols are written in normal/roman (upright) type without spacing
between the prefix symbol and the unit symbol e.g. MW, cm, km etc.
4. Symbols or units are not expressed in plural form. Thus we write 50 m or 7 erg
and not 50 ms or 7 ergs.
5. Not more than one solidus is used. For example 1 poise should be written as 1
poise = 1 g/s cm or 1 g s-1cm-1 and not 1g/s/cm.
6. Punctuation marks such as full stops are not written after the symbol of units,
e.g. 1 litre = 1000 cc (and not c.c.).
7. Some space is always to be left between the number and the symbol of the unit
e.g. 40 m (not 40m).
Significant figures
https://www.youtube.com/watch?v=b38hFWvEjwI
1. The digits that are known reliably plus the first estimated digit are known as
significant digits or significant figures.
6.1 cm
Normally, larger the number of significant figures in a measurement, greater is the
precision of measurement, and vice-versa.
Common Rules for Counting Significant figures
1. All non-zero digits are significant. E.g. 3.245 has 4 sig figs.
2. Zeros:
i) Trapped zeros: - All zeros occurring between two non-zero digits (also
known as trapped zero(s)) are significant no matter where the decimal point
is, if at all. E.g. 4.308 has 4 sig figs (sf).
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ii) Leading zeros: - If the number is less than 1, the zero(s) on the right of the
decimal point and to the left of first non-zero digit (also known as leading
zeros) are not significant. E.g. 0.023 has 2 sig figs.
iii) Trailing zeros: - In a number without a decimal point, the trailing zeros are
not significant. E.g. 3400 has 2 sig figs.
However, in a number with decimal point, the trailing zeros are significant.
E.g. 2.320 has 4 sig figs.
3. A choice of change of different units does not change the number of significant
figures in a measurement. E.g. 43.2 cm has 3 sig figs and 0.432 m also has 3
sig figs.
Sometimes there are some ambiguities E.g. 4.700 m (4 sig figs) = 470.0 cm (4
sig figs) = 4700 mm (2 sig figs) = 0.004700 km (4 sig figs).
To remove such ambiguities in determining sig figs, the best way is to report
every measurement in scientific notation (in the power of 10). Now the
confusion mentioned in above numbers disappears:
4.700 m = 4.700 × 102 cm = 4.700 × 103 mm = 4.700 × 10−3 km
Power of 10 is irrelevant to the determination of sig figs.
4. The multiplying or dividing factors which are neither rounded numbers nor
numbers representing measured values, are exact. They have infinite number
d
of significant digits, as per the situation. For example r = or s = 2πr, the
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factor 2 is an exact number and it can be written as 2.0, 2.00 or 2.000 as
required.
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