Unit-I
Measurements and units:
Definition of Physics
Physics is the natural science that studies matter, its motion and behavior through space and time, and the related entities of energy and force.
Need of physics
Physics helps us to organize the universe.
It deals with fundamentals, and helps us to see the connections between seemly disparate phenomena.
Physics gives us powerful tools to help us to express our creativity, to see the world in new ways and then to change it.
Physical quantities
A physical quantity is a property of a material or system that can be quantified by measurement.
A physical quantity can be expressed as the combination of a numerical value and a unit. For example, the physical quantity mass can be quantified as n kg, where n is the numerical value and kg is the unit.
A physical quantity possesses at least two characteristics in common, one is numerical magnitude and other is the unit in which it is measured.
Necessity of measurement of quantities
Measurements require tools and provide scientists with a quantity. A quantity describes how much of something there is or how many there are.
There are several properties of matter that scientists need to measure, but the most common properties are length and mass.
FPS, CGS, MKS and SI systems of units
The full form of four systemss of units used in measurements are
MKS system – Meter kilogram second system
In the MKS system, fundamental units are Meter, kilogram and second.
CGS system – Centimeter Gram Second system
In the CGS system, fundamental units are Centimeter, Gram and second
FPS system – Foot Pound second system
In the FPS system, fundamental units are Foot, Pound and second.
Features of each system of units and comparison of these systems of units
A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement in use include the International System of Units (SI), the modern form of the metric system, the British imperial system, and the United States customary system.
Necessity of a SI system of unitsEach system of unit should have relation between the other systems of unit.
Temperature has been converted in other systems.
Concept of least count of a measuring instrumentIn the science of measurement, the least count of a measuring instrument is the smallest and accurate value in the measured quantity that can be resolved on the instrument's scale.
In the science of measurement, the least count of a measuring instrument is the smallest and accurate value in the measured quantity that can be resolved on the instrument's scale.
For example, a sundial may only have scale marks representing the hours of daylight; it would have a least count of one hour. A stopwatch used to time a race might resolve down to a hundredth of a second, its least count. The stopwatch is more precise at measuring time intervals than the sundial because it has more "counts" (scale intervals) in each hour of elapsed time. Least count of an instrument is one of the very important tools in order to get accurate readings of instruments like vernier caliper and screw gauge used in various experiments.
Significant figure
various types of errors, their origins and the ways to minimize them. Our accuracy is limited to the least count of the instrument used during
the measurement. Least count is the smallest measurement that can be made using the given instrument.
For example with the usual metre
scale, one can measure 0.1 cm as the least value.
Hence its least count is 0.1cm.
Suppose we measure the length of a metal rod using a metre scale of least count 0.1cm.
The measurement is done three times and the readings are 15.4, 15.4, and 15.5 cm.
The most probable length which is the arithmetic mean as
per our earlier discussion is 15.43. Out of this we are certain about the digits 1 and 5 but are not certain about the last 2 digits because of the
least count limitation.
The number of digits in a measurement about which we are certain, plus one additional
digit, the first one about which we are not certain is known as significant figures or significant
digits.
Thus in above example, we have 3
significant digits 1, 5 and 4.
The larger the number of significant figures
obtained in a measurement, the greater is the accuracy of the measurement. If one uses the
instrument of smaller least count, the number of significant digits increases.
Rules for determining significant figures
1) All the nonzero digits are significant,
for example if the volume of an object is
178.43 cm3
, there are five significant digits
which are 1,7,8,4 and 3.
2) All the zeros between two nonzero digits
are significant, eg., m = 165.02 g has 5
significant digits.
3) If the number is less than 1, the zero/zeroes
on the right of the decimal point and to
the left of the first nonzero digit are not
significant e.g. in 0.001405, the underlined
zeros are not significant. Thus the above
number has four significant digits.
4) The zeros on the right hand side of the last
nonzero number are significant (but for
this, the number must be written with a
decimal point), e.g. 1.500 or 0.01500 have
both 4 significant figures each.
Concept and definition of scalar and vector quantities
A quantity which does not depend on direction is called a scalar quantity.
Vector quantities have two characteristics, a magnitude and a direction.
Scalar quantities have only a magnitude. When comparing two vector quantities of the same type, you have to compare both the magnitude and the direction.
Diagram :
