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MEASUREMENT AND UNIT

=> Any measurable or quantifiable property of the physical world is called a physical quantity.

=>Some physical quantities are length, mass, time, temperature, distance, etc.

=>Some unmeasurable physical properties are anger, love ,greed, hatred, etc.

=> Two types of physical quantities are there-Scalars and vectors.

=> Scalars are the physical quantities that are represented by their magnitude only and hence cannot be resolved into components .

=>Examples of scalar quantities include mass, time, length, energy, temperature, etc.

=>A vector is a physical quantity having a magnitude resolvable into multipath components and hence requires direction to be represented.

=> Examples of vectors include force, velocity, acceleration, etc. => Force needs to be defined in terms of magnitude in N and also the direction in which it acts.

=> Force needs to be defined in terms of magnitude in N and also the direction in which it acts.

=>Velocity is expressed in ms-1 and needs a direction in which the body is travelling.

=> The vector → Q can be subtracted from vector → P if it has a direction opposite to → P . The magnitude of the resultant vector will be equal to the difference of magnitudes of the subtracting vectors and the direction will be that of the greater vector.

=> Symbolically, a vector quantity is expressed as a line segment with an arrow. The length of the line segment represents the magnitude of the vector quantity whereas the arrow head and orientation of the line segment gives its direction.

=> A vector having a zero magnitude and arbitrary direction is called a null vector.

=> The result of the sum of a vector and its negative vector is always a null vector. A+ (-A) =0

=> Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard. This is called unit.

=> The result of a measurement of a physical quantity is expressed by a number (or numerical measure) accompanied by a unit.

=> Although the number of physical quantities appears to be very large, we need only a limited number of units for expressing all the physical quantities, since they are inter- related with one another. Besides , some physical quantities are arbitrarily regarded fundamental and can be used to form most other derived quantities.

=>The units for the fundamental or base quantities are called fundamental or base units. => The units of most physical quantities can be expressed as combinations of the base units. Such units obtained for the derived quantities are called derived units.

=>Physical quantities are either “scalar” or “vector” .

=>Vector quantities are important in the study of motion.

=> Some examples of vector quantities include force, velocity, acceleration, displacement, and momentum.

=>A quantity is a vector if it has a direction associated with it.

=>The speed is just the magnitude of the velocity in a certain direction. So speed is a scalar quantity, but velocity is a vector .

=>If a car has a velocity of 40 mph east, it has a speed of 40 mph.

=>A vector is drawn as an arrow with a head and a tail. The magnitude of the vector is often described by the length of the arrow. The arrow points in the direction of the vector. =>Vectors are generally written as boldface letters. They can also be written with an arrow over the top of the letter.

=>”The football player was running 12 miles an hour towards the end zone.”-

This is a vector because it represents a magnitude (12 mph) and a direction (towards the end zone). This vector represents the velocity of the football player. = “The volume of that box at the west side of the house is 12 cubic feet”. –

This is a scalar. The location of the box has nothing to do with the direction of the volume which has a magnitude of 12 cubic feet.

=> “ The temperature of the room was 15 degrees Celsius.” – This is a scalar, there is no direction.

=> “ The vehicle accelerated north at a rate of 4 meters per second squared.” –

This is a vector as it has both direction and magnitude. We also know that acceleration is a vector quantity.

=>Unit vectors are vectors with a magnitude of 1.

=>Unit vectors are used to define direction.

=>The credit for inventing vectors goes to Irish physicist William Rowan Hamilton.

=>Vectors can be defined in two dimensional or three dimensional space.

=>Three different systems of units for measurement -the CGS, the FPS (or British) system and the MKS system were in use extensively till recently.

=> In CGS system, the base units for length, mass and time were centimetre, gram and second respectively.

=>In FPS system , the base units for length, mass and time were foot, pound and second respectively.

=>In MKS system , the base units for length, mass and time were metre, kilogram and second respectively.

=>The system of units which is at present internationally accepted for measurement is the Système Internationale d’ Unites (French for International System of Units), abbreviated as SI.

=>In SI, there are seven base units.

=> Seven base units of the SI : metre (length), kilogram (mass), second (time), ampere (unit of electricity), kelvin (temperature), mole (amount of substance) and candela (light intensity).

=> Mnemonic for Seven base units of the SI = mksakmc

=>There is no physical quantity which has dimensions but no units. =Units are product of dimensional analysis.

=Units are product of dimensional analysis.

=> Besides the seven base units, there are two more units for two dimensionless physical quantities- plane angle and solid angle.

=>Plane angle is the ratio of length of arc to the radius.

=>The unit for plane angle is radian with the symbol rad .

=>The unit for the solid angle is steradian with the symbol sr. =>Both radian and steradian are dimensionless.

=>Both radian and steradian are dimensionless.

=>Both radian and steradian are dimensionless.

=>The definitions of base units are revised to keep up with the progress of the measuring techniques.

=> The metre (m) is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.

=> The kilogram (kg) is equal to the mass of the international prototype of the kilogram (a platinum-iridium alloy cylinder) kept at international Bureau of Weights and Measures, at Sevres, near Paris, France.

=>The second(s) 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. => The ampere(A) is that constant current which, if maintained in current two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2×10^–7 newton per metre of length.

=> The kelvin (K) is the fraction 1/273.16 of the thermodynamic dynamic temperature of the triple point of water.

=> The mole (mol) is the amount of substance of a system, which contains substance as many elementary entities as there are atoms in 0.012 kilogram of carbon – 12.

=> The candela (cd) is the luminous intensity, in a given intensity direction, of a source that emits monochromatic radiation of frequency 540×10^12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

=>Some units like mole are retained for general use (Though outside SI).

=> When mole is used, the elementary entities must be specified. These entities may be atoms, molecules, ions, electrons, other particles or specified groups of such particles.

=> A metre scale is used for lengths from 10^–3m to 10^2 m.

=>A vernier callipers is used for lengths to an accuracy of 10^–4 m.

=>A screw gauge and a spherometer can be used to measure lengths as less as to 10 ^–5m.

=>To measure lengths smaller than 10 –5m, we make use of some special indirect methods. => Large distances such as the distance of a planet or a star from the earth cannot be measured directly with a metre scale. An important method in such cases is the parallax method.

=>The parallax is the apparent displacement of an object as seen from two different points that are not on a line with the object.

=> If we look at a fixed object through a single eye while closing the other , with the change of eye the position of the object against some specific point on the background seems to change.This is a familiar example of parallax.

=>In parallax, the distance between the two points of observation is called the basis.

=In the simplest parallax example, the basis is the distance between the eyes.

=> To measure the distance D of a far away planet S by the parallax method, we observe it from two different positions (observatories) A and B on the Earth, separated by distance AB . We measure the angle between the two directions along which the planet is viewed at these two points.

=> To measure a very small size like that of a molecule (10^–8 m to 10^–10 m), we have to adopt special methods.

=> For visible light the range of wavelengths is from about 4000 Å to 7000 Å.

=>1 angstrom = 1 Å = 10^-10 m. =>As the wavelength of an electron can be up to 100,000 times shorter than that of visible light photons, electron microscopes have a higher resolving power than light microscopes and can reveal the structure of smaller objects.

=>As the wavelength of an electron can be up to 100,000 times shorter than that of visible light photons, electron microscopes have a higher resolving power than light microscopes and can reveal the structure of smaller objects.

=>As the wavelength of an electron can be up to 100,000 times shorter than that of visible light photons, electron microscopes have a higher resolving power than light microscopes and can reveal the structure of smaller objects.

=>The sizes of the objects we come across in the universe vary from the size of the order of 10^–14 m of the tiny nucleus of an atom to the size of the order of 10^26 m of the extent of the observable universe. =>1 fermi = 1 f = 10^–15 m

=>1 angstrom = 1 Å = 10^–10 m

=> 1 astronomical unit = 1 AU (average distance of the Sun from the Earth) = 1.496 × 10^11 m

=> 1 light year = 1 ly= 9.46 × 10^15 m (distance that light travels with velocity of 3 × 10^8 m s–1 in 1 year)

=>Parsec is the distance at which average radius of earth’s orbit subtends an angle of 1 arc.

=>The parsec equals 3.26 light-years.

=>1 astronomical unit = 1.581 × 10-5 light-years.

=>The prefixes are used in very small as well as very large quantity.

=>Physics deals with matter, energy and their interaction.

=A microgram or microgramme (μg) is equal to one millionth (1×10^−6) of a gram.

=A microgram or microgramme (μg) is equal to one thousandth of a milligram. [{(µg comes from the Greek letter mu, where µ means “small”.)}] => 32 × 10^-10 kg =3.2 µg.

=>The quantities 123.0,12.30,1.230, 2.000 and .2000 all contain 4 significant figures.The first three numbers are known with certainty and the final number is always taken as significant.

=> A zero used to fix a decimal point is never significant.

=>A trailing zero to “count” as significant, must be followed by a decimal.

=>Writing just “5000” would give us only one significant figure i.e. 5.

=>The quantities 0.456, 0.0456 , 0.00456 and 45600 all contain 3 significant figures.All exponential zeros are insignificant. =>0.000000001 has only one significant figure; the remaining zeros were used to fix the decimal point.

=>Significant figures in 0.02020=5.

=>Significant figures in 70.010=5

=>Significant figures in 0.03000=4

=>As an exponential number 0.03000 can be represented as 3.000 x 10^-2.

=>Zeros within a number are always significant.

=>The quantities 609, 60.9, 6.09 and 0.609 all contain 3 significant figures since the 0 between the 6 and 9 is significant. The number 609 means that the true value rests somewhere between 608 and 610, thus, the zero is known with certainty and is significant.

=> The number of significant digits in 0.073 =2.

=>Geophysics deals with the study of internal structure of earth.

=> A physical balance is a modified beam balance to measure small masses more accurately by comparison.

=>Amount of a substance in terms of numbers is measured in mole.

=>While measuring length the eye must be kept above the scale.

=>A screw guage measures the diameter of a wire or the thickness of a metal sheet. =>The study of the nature of heat, modes of transfer and effects of heat is studied under the branch named as heat .

=>The number 0.0000748 in scientific notation is 7.48 * 10^ -5.

=>Non-zero digits are always significant .

=> The quantities on the basis of which other quantities are expressed are called base quantities .

=>Plasma physics deals with the production and properties of the ionic state of matter .

=>A stop watch measures the time interval of an event .

=> The amount of substance is a base quantity.

=>A spring scale can not measure mass, only weight.

=> Object’s mass when measured with the same beam balance and standard mass is the same everywhere.

=> Object’s weight even when measured with the same spring scale varies with gravity.

=> A weighing scale actually measures the value of Normal Reactions acting on it. => N (Normal Reaction) =mg.

=> The weighing scales are measured in ‘KG’ instead of ’N’ (Newton) because the calibration scale is set to 1: 9.81 ratio.

=> 981 N force on spring scale is displayed as 100 kg ,the mass part only.

=> g= 9.81 N/m2 on the earth. =>Spring scale shows different value of mass on another planet.

But a two-pan balance gives the same reading.

=> Weighing Scales actually output weight depending on the force exerted on it, but displays it as mass (just by dividing it by a constant=9.8).

=> We need to multiply the displayed value on a spring scale by 9.8 to calculate the actual Weight in SI units.

=>10kg*9.81m/s2=98.1N is shown as 10 kg by a spring scale.

=> In a gravityless environment, a weighing scale is useless to measure mass.

=> In a gravityless environment, we use an inertial balance. For a given stiffness (spring constant) of the spring; the frequency of vibration of the spring calculates the mass of a body.

=> Unlike a spring scale ,a beam balance directly measures mass.

=> A spring scale measures weight by reporting the distance that a spring deflects ( Hooke’s law) due to a load under gravity.

=>The deflection is proportional to the force (weight) which in turn is proportional to the mass.

=> Smallest measurement an electronic balance can take is 1/1000 g = 0.001 g .

=> A measuring cylinder is a graduated glass cylinder marked in millilitres.

=> The science that deals with the study of non-living things is known as physical science .

=>The least count of screw gauge is 0.01 mm.

=> A refrigerator is made on the principles of thermodynamics .

=>The distance of moon from earth is 3.84 * 10 8 m.

=> In screw gauge a thimble around its one end has 100 divisions.

=>One division of Vernier scale is of 0.9 mm .

=> If zero line of the vernier scale is on the right side of the zero of the main scale, then zero error will be positive .

=>Zeros used for spacing the decimal point are non-significant .

=>All the accurately known digits and the first doubtful digit in an expression are known as significant figures .

=> The final zeroes after decimal are significant.

=> The least count of physical balance is 0.01 g.

=>The study of fourth state of matter is called plasma physics.

=>An interval of 300µs is equal to 3 × 10 -4 s.

=> An instrument used to measure small lengths such as internal or external diameter or length of a cylinder, etc. is called vernier callipers.

=>The prefix for 4800000 W is 4800 kW.

=> In screw guage, the distance between consecutive threads on the spindle is 1 mm.

=> All physical quantities are measurable.

=> A worldwide system of measurements in which the the units of base quantities were introduced is called international system of units .

=>By converting 3 700 000 Watt into kilowatt, we get 3 700 kW .

=> The study of motion of objects, its causes and effects is called mechanics . => Harry claimed that the diameter of a wire is 1.042 using vernier callipers. Upto what extent he is right is 1.04 cm.

=> The words or letters added before a unit and stand for the multiples or sub-multiples of that unit are called prefixes.

=>10 vernier scale divisions coincide with 9 main scale divisions.

10 vsd=9 msd

1 vsd=.9 msd

LC= 1MSD-1VSD

LC=1MSD-.9MSD=.1MSD ( .1 mm).

=> The least count of Vernier calipers is 0.01 cm=0.1 mm.

=>The “seconds in a day” can be written in standard form as 8.64 × 10 5 s .

[{(A day,243 Earth days, on Venus lasts longer than a year, 225 Earth days.)}]

=>A digital wrapper is 4.5 cm long and 5.9 cm wide. Its area upto significant figures will be 26.55 cm².

=>Physical sciences were divided into 5 disciplines.

=>The smallest change a sensitive beam balance can record is 100 mg.

=> By using prefixes, we can write 335 × 10 -8 s as 3.35 µs .

=>When a standard is set for a quantity, then the standard quantity is called a unit .

=> The study of the internal structure of the Earth is known as geophysics.

=>A fundamental quantity belongs to a typical class, each of them having no dependence with other fundamental quantities.

=>The typical attribute that is common to a class of physical quantities is what is called their dimensionality.

=>A typical dimension represents

a typical class of physical quantities.

=>The dimension of a body means how it is relatable in terms of base quantities.

=> The dimension of a physical quantity is represented by the powers to which the fundamental quantities are raised.

=> The seven fundamental quantities are enclosed in square brackets [ ] to represent its dimensions.

=> The dimension of Length is described as [L].

=> The dimension of time is described as [T].

=> The dimension of mass is described as [M].

=> The dimension of electric current is described as [A].

=> The dimension of the amount of quantity can be described as [mol].

=> The dimension of temperature is [K].

=> The dimension of luminous intensity is [Cd].

=> The volume of a solid is the product of length, breadth and its height.

As volume is dependent on mass and time, the final dimension of volume will be [M]0[L]3[T]0