Units Flashcards
For a quantity to be a physical quantity:
It should be measurable.
It should explain physical happenings
It should express physical happenings in form of laws.
Why are emotions not a physical quantity
It is not measurable.
Physical quantity is represented by
Q
In a physical qty the relationship between its magnitude and unit.
Magnitude is inversely proportional to the unit.
3 types of physical quantities
Ratio (magnitude only)
Scalar (magnitude and unit)
Vector (magnitude,unit and direction)
Physical quantity in form of ratio of 2 similar quantities have no
Units.
E.g. Relative density =
Density of object/Density of water (4°C)
(Exception : Angle)
E.g. of physical quantities in form of ratio of 2 similar quantities
Relative density
Refractive index
Angle.
Mass of the electron and the sun
Electron : 9.1 x 10 raised to -31
Sun : 2 x 10 raised to 30 (ntomo)
1 mile = ……… km
1.6 (d - j)
Fermi short form
fm
Chandra Shekhar unit short form
CSU
Astronomical unit short form
A.U
X-ray unit short form
XU
1 X-ray unit =
10 raised to -13 m.
do : dm
1 light yr
9.46 x 10 raised to 15 m.
b-rj , to:tL
Bridge total.
Parsec short form
pc
1 CSU :
1.4 times the mass of sun = 2.8 x 10³⁰
n-v, do:mo
Envy domo
1 pc =
3.26 light yrs.
1 metric tonne =
1000 kg.
1 quintal =
100 kg.
1 amu =
1.67 x 10⁻²⁷
Work dimensional formula
ML²T⁻²
C.G.S unit of work
erg
1 joule = ……… ergs
1 crore ergs.
10 million ergs
Many physical quantities have the same …..
Dimensions
We round off measurements on the basis rules established by
Convention.
Absolute error in the measurement of a physical quantity is
The difference between the true value and the measured value.
Fundamental physical quantities also called as
Absolute quantities or Base quantities.
3 properties of fundamental quantities
Independent of all other quantities
Do not require help of any other physical qty for their definition
Expresses other quantities.
CGS system of units is also called as
Gaussian system of units.
In the earlier systems of units, the fundamental qtys were only :
Length, mass and time.
MKS system is also called as
Giorgi system.
In FPS system, the unit of force is
Poundal
1 lunar month = …… days
27.3
Lunar month definition
Time taken by the moon to complete 1 revolution around the Earth
1 Shake =
10⁻⁸ seconds.
SI system is also known as
International system of units
No of fundamental qtys in SI system
7
7 Fundamental qtys in SI system
M E T(2) A L(2)
Luminous intensity is measured in
Candela (cd)
1 kg = ………… atoms
5.0188 x 10²⁵ atoms of carbon 12.
1 kg is taken as the mass of a ….
Cylinder made of platinum-iridium alloy kept at International Bureau of Weights and Measures at Sevres near Paris,France.
Symbol of impulse
I
Pressure and Power is represented commonly by the same symbol
P
Linear momentum is represented by
p
Kinetic energy symbol and unit
Unit : joules
Symbol: KE
- 251 is rounded as
- 25 is rounded as
- 35 is rounded as
- 3 (5 is followed by numbers greater than 0)
- 2 (the preceding digit is even : 2)
- 4 (preceding digit is odd : 3)
Unit and symbol of electric charge
Unit : Coulomb
Symbol : q
Electric current unit and symbol
Unit : Ampere
Symbol : I
Power SI unit and symbol
Unit : Watt
Symbol : P
Pressure unit
Pascal
Electric potential unit and symbol
Symbol : V
Unit : Joules/Coulomb
ML²T⁻² is the dimensional formula of
Work,energy,torque.
Significant figures definition
Significant figures in the measured value of a physical qty tell the number of digits in which we have confidence.
Larger the number of significant figures obtained in a measurement greater is the
Accuracy
Rules observed in counting the number of significant figures
All non zero digits are significant
A zero becomes significant only if it is between 2 no zero digits or if situated in the right side of the number.
In exponential notation, the numerical portion gives the number of significant figures.
No of significant figures in
1.32 x 10⁻²
3 (only take the numerical portion)
Absolute error in the measurement of a physical qty is the
Magnitude of difference between the true value and the measured value.
Absolute error can be both
Positive and negative.
If the true value of a physical quantity is unknown then how would we calculate it
1) we measure the physical quantities n times.
2) take the arithmetic mean of all these measurements.
3) this mean value is taken as the true value of the physical qty.
Mean absolute error is represented by
___
∆a
Mean absolute error is the
Arithmetic mean of all the magnitudes of absolute errors.
Relative density =
Density of object/Density of water at 4°C
Refractive index =
Velocity of light in air / velocity of light in medium.
Exceptional physical qty in the form of ratio
Angle = arc/radius
Even though it has only a numerical value a unit such as degrees or radians is also used.
Physical qtys that are neither scalar nor vector are called
Tensors
System of units definition
It is a COMPLETE SET of units ; including both fundamental and derived units ; used for representing all kinds of physical quantities.
1 metre is defined as the the distance travelled by light in a time interval of
1/299,792,458 part of a second.
np pk pn RLV
Exa,peta,tera,giga,mega are represented by
E,P,T,G,M
pico,femto,atto are represented by
p,f,a
Name SI prefixes
Exa,peta,tera,giga,pico,femto,atto etc.
Derived quantities are expressed as a
Product of differ powers of the fundamental qtys.
Spring constant unit and symbol.
Symbol : k
Unit : Newton/metre
Gravitational constant unit and symbol.
Symbol : G
Unit : N m²/ kg²
Intensity of gravitational field unit and symbol
Symbol : E[g]
Unit : N/kg
Gravitational potential unit and symbol
Unit : V[g]
Symbol : Joules/kg
Surface tension unit and symbols
Symbol : T
Unit : N/m or Joules/m²
Temperature symbol and unit
Symbol : T
Unit : Kelvin
Heat symbol and unit
Symbol : Q
Unit : Joules
Specific heat symbol and unit
Symbol : c
Unit : Joules/kg-K
Thermal capacity symbol and unit
Symbol : C
Unit : Joules/K
Latent heat symbol and unit
Symbol : L
Unit : Joules/kg
Dimensions of a physical qty
Powers to which fundamental quantities must be raised in order to express the given physical quantity.
Dimensional equation e.g.
[force] = [MLT⁻²]
In a dimensional equation such as
[force] = [MLT⁻²] ; the square brackets are used to indicate that
The equation is among the dimensions and not among the magnitudes.
Dimensional formula vs dimensional equation
Dimensional formula:
[force] = [MLT⁻²]
Dimensional equation
(RHS of the formula):
[MLT⁻²]
Derived qtys
All other physical quantities that can be derived by suitable multiplication or division of different powers of the fundamental quantities.
The supplementary units are
Radians (rad) for plane angle
Steradian (sr) for solid angle
1 metre is defined as
The distance containing certain no of wavelengths of light.
Here the light is :
Orange red light emitted by an atom of krypton-86.
The no of wavelengths:
1650763.73
(d - gl - ok - gn - kn)
Density symbol an unit
Symbol : d
Unit : kg/m*3
Angular displacement unit and symbol
Symbol : θ
Unit : Radians (rad)
Angular velocity symbol and unit
Symbol : ω (omega)
Unit : Radians/sec
Angular acceleration symbol and unit
Symbol : α
Unit : Radians/sec*2
Permittivity of free space symbol and unit
Symbol : ε₀
Unit : (Coulomb)2 / Newton-meter2
Resistance symbol and unit
Symbol : R
Unit : Volt/Ampere or ohm
Resistivity symbol and unit
Symbol : ρ (rho)
Unit : ohm-meter.
The principle used to check dimensional correction of a given physical relation :
Principal of homogeneity.
Principal homogeneity :
According to this principle, the dimensions of EACH TERM in a physical relation should be same.
E.g.
X = A ± (BC)² ± √(DEF)
[X] = [A] = [(BC)²] = [√(DEF)]
Even though the a physical relation is dimensionally correct it does not mean that it is always
Physically correct.
Measuring process is essentially a process of
Comparison.
The FINAL RESULT OF MEASUREMENT is written as
___
a = true value ± ∆a
___
∆a : mean absolute error.
Here the true value is actually the mean value of all the observations.
The fundamental quantities in mechanics are
Length , mass and time
The fundamental quantities of mechanics (length,mass and time) are arbitrarily chosen ?
In fact any three quantities in mechanics can be termed as fundamental quantities.
E.g.
If speed and time are fundamental qtys, then length would become a derived quantity (speed x time).
Mole :
Amount of substance that contains as many elementary entities as the no of atoms in .012 kg of Carbon 12.
Moment of inertia symbol and unit
Symbol : I(i)
Unit : kg-mg*2
Torque symbol and unit
Symbol : τ (tau)
Unit : Newton-metre
Angular momentum symbol and unit
Symbol : L
Unit : Joule-sec
Conductance symbol and unit
Symbol : G or 1/R
Unit : ohm⁻¹
Conductivity symbol and unit
Symbol : σ, 1/ρ
Unit : ohm⁻¹ meter⁻¹
Intensity of electric field symbol and unit
Symbol : E
Unit : volt/metre ; Newton/Coulomb
Fundamental units ?
Any unit used for a fundamental qty.
E.g. light yr
Gas constant symbol and unit
Symbol : R
Unit : Joule / kg-K
Boltzmann constant symbol and unit
Symbol : k
Unit : Joule/K
Coefficient of thermal conductivity symbol and unit
Symbol : K
Unit : Joule /m-s-K
Stefan’s constant symbol and unit
Symbol - σ
Unit - joule/m²-K⁴
Wien’s constant symbol and unit
Symbol : b
Unit : Watt-meter
Permeability of free space symbol and unit
Symbol : μ
Unit : Newton/ampere*2
In addition or subtraction of observations of various measurements, the no of decimal places taken for the resultant is
The number of least decimal places found in the observations.
In multiplication or division of observations of various measurements, the no of significant figures taken for the resultant is
The number of least significant figures found in the observations.
The absolute is the magnitude of difference between the
True value (mean value) and measured value.
Relative error is also known as
Fractional error
Relative error is defined as the
Ratio of the mean absolute error to the mean value.
Percentage error is just the
Fractional error represented in %
Sidereal vs Solar day
An Earth day can be measured in different ways.
Measure the time it takes for a complete rotation of Earth around its axis.
Measure the time it takes for the Sun to appear in the same meridian in the sky. This interval is known as the solar day.
Measure the time it takes for a distant star to appear in the same meridian in the sky. This interval is known as the sidereal day. The time interval mentioned in (1) is equal to the sidereal day. Why?
Because these stars aware very distant.
1 complete rotation of Earth around its axis takes 23 hours, 56 minutes and 4.1 seconds
Sidereal day is also 23 hours, 56 minutes and 4.1 seconds by definition.
Solar day is longer than the sidereal day
Earth moves a little less than a degree around the Sun during the time it takes for 1 full axial rotation. So, for the Sun to appear on the same meridian in the sky again after 1 full axial rotation, the Earth has to rotate one extra degree to bring the Sun into the same apparent meridian in the sky. This is why the solar day is longer than the sidereal day by about 4 minutes.
Sidereal day is shorter than solar day by
Approx. 4 min
1 solar year = ……….. avg solar days
365.25
1 solar yr = ………. sidereal days
366.25
Why does the duration of solar days vary
Earth’s orbit is an ellipse so the Earth moves faster on its orbit around the Sun when it is nearest the Sun (perihelion) and slower when it is farthest from the Sun (aphelion). This causes the duration of solar days to change.
Coefficient of self induction symbol and units
Symbol : L
Unit : Volt-second/Ampere
Magnetic flux unit
Units : Volt-second
Weber
Henry
Code for symbols of mechanical qtys
A4 VAD PIG
KE,F2,Eta
