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Important Equations in Physics (AS)
Unit 1: Quantities and their measurements (topics 1 and 2 from AS syllabus)
1 System of units M.K.S system, C.G.S. system, F.P.S. system and SI system
meter, kilogram, second centimetre, gram, second foot, pound, second
2 SI system Base units Length m etre^ Mass K ilo g ram^ Time s econd^ Temp kelvin( K )^ Current ampere( A )
luminous intensity candela ( Cd )
Amount of substance mol e 3 Multiples of units
Tera T 1012
Giga G 109
Mega M 106
Kilo K 103
Deci d 10 -^1
centi c 10 -^2
milli m 10 -^3
micro μ 10 -^6
nano n 10 -^9
pico p 10 -^12
femto f 10 -^15
atto a 10 -^18 4 Celsius to kelvin conversion K= θ
oC +273.15 Add to 2^7 3.15 to Celsius scale to convert to kelvin scale 5 Accuracy To find the accurate value, we need to know the true value of a physical quantity. Nothing can be measured absolutely accurate. 6 Precision ...value close to the true value. Can be increase by sensitive instrument. 7 Error Systematic: due to faulty apparatus Random: due to experimenter 8 Calculation error For sum Q=a+b ΔQ=Δa+Δb
For difference Q=a-b ΔQ=Δa+Δb 9 Calculating error For product Q=a×b
∆ ܳ = ൬
൰ ×ܳ
For division Q=a/b ∆ܳ = ൬
൰ ×ܳ
10 Significant figures (sf) examples
four sf
two sf
1002 four sf
three sf
one sf
two sf
three sf
two sf
190 2 or 3 sf 11 Uncertainty ∆ value
the interval of confidence around the best measured value such that the measurement is certain not to lie outside this stated interval ݉ ݁ ܽ ݏݑݎ݊݁݉݁ ݐ = ܾ ݁ݐݏ ݉ ݁ܽ ݏݑݎ݀݁ ݒ݈ܽ ݁ݑ ± ݑ݊ ܿ݁ݎ ݊݅ܽݐ ݐݕ 12 Percentage and relative uncertainty ݁݃ܽݐ݊݁ܿݎ݁^ =^
× 100
× 100
13 Vector and scalar quantities Vector direction eg.^ →^ magnitude with unit and velocity, force etc
Scalar → only magnitude with units Eg. density, pressure, speed, distance etc 14 Magnitude of resultant vector c of two vectors a and b
a and b same direction: apply simple addition a and b opposite direction: apply simple subtraction ⊥ to each other: apply Pythagoras theorem ܿ = √ܽ ଶ^ + ܾ ଶ Not ⊥ to each other: apply cosine rule ܿ ଶ=ܽ ଶ^ + ܾ ଶ^ − 2 × ܽ × ܾ × ܿݏ ߛ 15 Direction of resultant vector c of two vectors a and b
a and b in same direction then c is also the in the same direction a and b opposite direction then c is in the direction of bigger vector
⊥ to each other apply ߠ = tanି ଵ^
Not ⊥ to each other: use protractor 16 Components of vector F making θ with x - axis
x- component ۴ܠ = ۴ × cos ߠ
y-component ۴ܡ = ۴ × sin ߠ 17 Measurement by cathode ray oscilloscope (cro)
Time base: horizontal scale or x-axis
Vertical gain: vertical scale or y-axis
Unit 2: Motion, force and energy (topic 3, 4, 5 and 6 from AS syllabus)
1 Average velocity ݒ̅ (^) ݒ̅ = ݏ ݐ
s is the displacement in meters and t is the time in seconds. 2 Instantaneous velocity Velocity of an object at any particular instant of time. 3 Average acceleration ܽ ത (^) ܽ ത = ∆ݒ ∆ݐ
Δv is the change of speed and Δt is the change of time. Unit of acceleration is ms-^2 4 Acceleration and velocity Same direction: acceleration is +ve (if velocity is in +ve direction) Opposite direction: acceleration is - ve, deceleration, retardation 5 Graphical representation
6 Speed-time graph Area under the graph: distance covered by and object Gradient of the graph: acceleration 7 Distance-time graph Gradient of the graphs: speed of an object 8 Equation for uniform motion, constant motion
only use when acceleration= 0 and no net force is applied 9 Equations for uniformly accelerated motion
- body start motion u=
- body come to rest v=
- free fall g=a=9.81ms-^2
- horizontal motion s=x
- vertical motion s=h=y
ଶ ݒଶ^ = ݑଶ^ + 2 ܽݏ
v is the final velocity in ms-^1 , u is the initial velocity in ms-^1 , s is the distance/displacement in m, a is the acceleration in ms-^2 and t is the time in s.
10 Friction → static and dynamic
Static ݂ ௦ = ߤ௦ ×ܰ Dynamic ݂ = ߤ ×ܰ N is the reaction or normal force perpendicular to the surface
fs is the static friction in newton, fk is the dynamic friction in newton, μs is the coefficient of static friction μk is the coeff. of dynamic friction 11 Air resistance or viscous force or viscous drag
- Opposing force to the motion in presence of air or fluid
- During free fall in the beginning: weight≫air resistance+upthrust
- Later: weight> ݅ܽݎ resistance+upthrust 12 Terminal velocity (^) - at terminal velocity, weight= air resistance + upthrust 13 Projectile: Motion in two dimensions, v and angle θ with horizontal, upward is +
x-component → no acceleration ݒ௫ = ݒ cos ߠ ݔ = ݒ௫ ݐ = ݐݒ cos ߠ
y-component → acceleration is g ݒ௬ = ݒ sin ߠ ݕ = ݒ௬ݐ − ½݃ ݐ ଶ
horizontal range ܴ =
max range at θ=45 o 14 Weight and mass: weight is force of gravity, mass is the amount of matter, it never changes
ݓ = ݉ ×݃
w is the weight in newton (N), m is the mass in kg and g is acceleration due to gravity=9.81 ms-^2
15 Stability of an object Lower the centre of gravity →more stable the object is Wider the base of an object →more stable the object is 16 Momentum Momentum=mass×velocity p = m × v
unit is kg.m.s-^1 or N.s
17 Conservation of linear momentum
Total momentum before collision = total momentum after collision ݉ ݑ + ݉ ݑ = ݉ ݒ + ݉ ݒ 18 Elastic collision Total kinetic energy before collision =total kinetic energy after collision ½݉ (^) ݑ^ ଶ^ + ½݉ (^) ݑ^ ଶ^ = ½݉ (^) ݒ^ ଶ^ + ½݉ (^) ݒ^ ଶ 19 Elastic collision (^) for two masses ݉ ≠ ݉ or ݉ = ݉ the equation must satisfy ݑ + ݑ = ݒ + ݒ
38 Internal energy: Sum of the Ek and Ep of the molecules of a system
∆ܳ = ∆ܷ + ∆ܹ ΔQ heat applied,^ ΔU increase in the internal energy and ΔW is the work done by the system 39 Power ܲ =
P is the power in watts, W is the work done, F is the force and t time
40 Efficiency of a machine (^) ݕ݂݂ܿ݊݁݅ܿ݅ܧ = ݈ݑ݂݁ݏݑ^ ݁݊݁ ݕ݃ݎ^ ݐݑݐݑ ݈ܽݐݐ ݁݊݁ ݕ݃ݎ ݊݅ ݐݑ × 100 Efficiency expressed as^ can be percentage
Unit 3: Electric charge (topic 17, 19 and 20 from the syllabus)
1 Electric field intensity E: force on a unit charge q at any point around another charge Q
..between the two parallel plates ܧ =
.. uniform between the plates separation d, unit is Vm-^1
..due to point charge Q on charge q ܧ =
.. decreases with distance increase, unit is NC-^1 2 Current: Rate of flow of charges in a conductor ܫ^ =
(^) ݐ^ I is the current in amp Q is the charge in coulombs (C)eres^ (A), t is the time in seconds (s) 3 Current path In circuits the current always choose the easiest path 4 Conduction of electric charge
..in electrolyte liquids due chemical reaction, ions → electrolysis ..in liquids (eg mercury) or solids (metals) due to free electrons → conduction 5 Ohms law Voltage across the resistor is directly proportional to current, V ⋉ I or ܸ ܫ
V is the voltage in volts (V), I is the current in amperes (A) and R is resistance in ohms (Ω)
6 Voltage Energy per unit charge
ܸ =
Q is the charge in coulombs (C), V is the voltage in volts (V) Energy is in joules (J) 7 Electromotive force(emf) e.m.f. = lost volts + terminal p.d. e.m.f.=Ir+IR unit of emf is volts (V)
the energy transferred to electrical energy and when 1 C charge passes through a circuit_._ 8 Max. Power dissipated by the cell ܲ =^
Max. power P when R=r, E is the emf
9 Resistance and resistivity (^) ܴ = ߩ ܮ ܣ ρ is the resistivity of resistor in Ω.m
R is the resistance a resistor, L is the length of a resistor in meters A is the area of cross-section of a resistor in m^2 10 Circuit In series circuit → the current stays the same and voltage divides In parallel circuit → the voltage stays the same and current divides 11 Resistance in series (^) ܴ = ܴ ଵ + ܴ ଶ + ܴ ଷ + ⋯ R, R 1 , R 2 and R 3 are resistances of 12 Resistance in parallel (^1) resistor in ohms ܴ
ܴ ଵ^ +^
ܴ ଶ^ +^
ܴ ଷ^ +^ ⋯
13 Potential divider ܸ ଵ ܸ ଶ
ଵ ܴ ଶ
V 1 voltage across R 1 V 2 voltage across R 2 14 Potential divider (V total voltage) ܸ ଶ^ =^ (
ଶ ܴ ଵ + ܴ ଶ
) × ܸ ܸ ଵ = (
ଵ ܴ ଵ + ܴ ଶ
) ×ܸ
15 Power (^) ܲ = ܫ × ܸ ܲ = ܫଶ (^) ×ܴ (^) ܲ =
ܸ^ ଶ
(^) P is the power in watts (W)
16 Power (^) ܲ = ݕ݃ݎ݁݊ܧ ݁݉݅ݐ
The unit of energy is joules (J)
17 I-V Characteristics metals I ↑, V↑
diode I in one direction
filament V ↑,T↑,R↑,I↓
thermistor T ↑, R↓, I↑
LDR
L ↑,R↓.I↑
18 Kirchhoff`s law ∑I = 0 ∑EMF = ∑IR 19 Cathode rays Stream of electrons emitted from heated metal (cathode) are called cathode rays and the process of emission is called thermionic emission.
18 Strain energy per unit volume =^
×
×
2 ×^ ݏݏ݁ݎݐݏ^ ×^ ݊݅ܽݎݐݏ
The area under the stress-strain graph is called strain energy per unit volume. The unit of energy is joules (J).
19 Ductile and brittle material
Ductile: → drawn into wire without breaking → small elastic region and large ductile → eg copper wire
Brittle: → cannot drawn into wire → small or large elastic region but small ductile region, eg glass
Unit 4: Nuclear physics (topic 27 from the syllabus)
1 Elementary particles of an atom
Proton: Positive charge, inside the nucleus, same mass as neutron
Electron: negative charge, revolve around the nucleus, mass is 1/1836 of proton
Neutron: no charge, inside the nucleus, same mass as proton 2 Nucleon no ‘A’ also called mass number or atomic weight, it is sum of protons and neutrons 3 Proton no ‘Z’ also called atomic number, total number of protons 4 Alpha particles α - particles
Helium nucleus Stopped by paper Highest ionization potential
ଶ^ ସ^ ݁ܪ
or ଶ^ ସ^ ߙ 5 Beta-particles β - particles
Fast moving electrons Stopped by aluminum Less ionization potential
ି ଵ^ ݁
or ି ଵ^ ^ ߚ 6 Gamma-particles γ - particles
Electromagnetic radiation Only stopped by thick a sheet of lead Least ionization potential
^ ^ ߛ
7 Alpha decay (^) ܺ (^) ⇒ ିି (^) ଶସܻ (^) + (^) ଶ ସ݁ܪ (^) + ݁݊݁ݕ݃ݎ Parent nuclei X emit two protons and two neutrons to make alpha particle 8 Beta decay ^ ܺ^ ⇒^ ା^ ଵܻ^ +^ ି ଵ^ ߚ^ +^ ݁݊݁ݕ݃ݎ
In parent nuclei X one of the neutrons changes into neutron and electron. The electron emits as beta 9 Gamma decay (^) ܺ ^ ^ ⇒^ ^ ܻ^ +^ ^ ߛ^
Gamma decay is the simple loss of energy from the nucleus 10 Radioactivity is a spontaneous process
Does not depend upon the environmental factors eg atm. Pressure, temperature, humidity, brightness etc 11 Radioactivity is a random process
All the nuclei have equal probability of decay at any time, cannot predict which nucleus will emit radiation. 12 Half-life Time in which the activity or mass of a radioactive substance becomes half 13 Atomic symbol
Examples: (^) ଵ^ ଵܪ^ , ଵଶܥ^ , ଵ଼ܱ
A is the total no of protons and neutrons Z is the total no of protons
14 Isotopes Elements having atoms of same number of protons but different number of neutrons Eg^ ܥ
ଵଶ (^) , ଵସܥ (^) or (^) ଵ ଵܪ (^) , (^) ଵ ଶܪ (^) , (^) ଵ ଷܪ (^) or ଶଷହ ଽଶܷ (^) , ଶଷଽଽଶ (^) ܷ ,
Unit 5: Waves (topic 15 and 16 from the syllabus)
1 Wave equation 1 ݒ = ݂ × ߣ v is the speed of wave in ms-^1 f is the frequency in Hz λ is the wavelength in metre 2 Wave equation 2 (^) ݂ = 1 ܶ
(^) T is the time period of wave in second 3 Movement of the particles of the medium
Longitudinal waves=> back and forth same direction as waves Transverse waves=> perpendicular to the direction of waves 4 Wavelength ′ߣ′ Distance between two crests or two troughs, unit metre (m) 5 Frequency ‘f’ Total number of waves in one second, unit hertz (Hz) 6 Time period ‘T’ Time taken for one complete wave, unit second (s) 7 Speed of wave motion ‘v’ Distance move by crest in direction of wave in 1second, unit ms-^1 8 Displacement of particle ‘s’
Distance move by a particle from its mean position in either direction, unit metre (m) 9 Amplitude ‘a’ The maximum distance move by the particle, unit metre (m) 10 Wave fronts Representation of crests of a wave by straight line perpendicular to the direction of wave. Distance between two wave fronts is wavelength. 11 Progressive wave Continuous waves created by a source 12 Phase difference When the crests and troughs of two waves do not overlap each other then two waves have phase difference 13 Coherent waves Two waves of same properties and originate from same source 14 Intensity of a wave ‘ I’ (^) ܫ = ܲ ܣ Unit of intensity is Wm-^2
P the amount of wave energy per second at particular point falling on surface area A 15 Intensity of a wave ‘I’ Intensity of wave is directly proportional to the amplitude square ܫ ⋉ ܽ ଶ 16 Compression region When particles of a medium come close to each other 17 Rarefaction region Where particles of a medium move further apart from each other 18 Diffraction When waves pass through a narrow gap, they spread out. 19 Interference of light waves Constructive interference: When the crests-crests and troughs-troughs of two waves overlap each other, amplitudes become added
Destructive interference: When crests-troughs of two waves overlap each other, amplitudes cancel each other
20 Young double slit experiment
For bright fringes: ݔ =
For dark fringes: ݔ =
a is the distance between the two slits, D is the distance between slits and the screen, λ is the wavelength of light, n is the order of bright or dark fringe counting from the first bright fringe at the centre, x is the distance of nth fringe from the centre 21 Diffraction grating ݀ ݊݅ݏ ߠ = ݊ߣ
d is the gap between two grating lines, θ is the angle of the order of maxima, n is the order of a maxima and λ is the wavelength 22 Polarized light When the electric and magnetic field of light waves oscillates only in one dimensions, this process of transforming un-polarized light into polarized light is called polarization. 23 Standing or stationary waves
A wave results when two waves which are traveling in opposite direction, and which have the same speed and frequency and approx. equal amplitudes, are superimposed (overlapped)
