Important Equations in Physics As

1

Important Equations in Physics (AS) Unit 1: Quantities and their measurements (topics 1 and 2 from AS syllabus)

1

System of units

2

SI system Base units

3

Multiples of units

4 5

Celsius to kelvin conversion Accuracy

6 7 8

Precision Error Calculation error

9

Calculating error

10

Significant figures (sf) examples Uncertainty ∆value

11

M.K.S system, C.G.S. system, F.P.S. system and SI system Length metre

Tera T 12 10

Giga G 9 10

12

Percentage and relative uncertainty

13

Vector and scalar quantities

14

15

16 17

Magnitude of resultant vector c of two vectors a and b Direction of resultant vector c of two vectors a and b Components of vector F making θ with x -axis Measurement by cathode ray oscilloscope (cro)

meter, kilogram, second centimetre, gram, second foot, pound, second

Mass ilo gram K ilo

Mega M 6 10

Time second

Kilo K 3 10

Deci d -1 10

Temp kelvin( K ) centi c -2 10

milli m -3 10

luminous intensity candela (Cd )

Current ampere( A) micro µ -6 10

nano n -9 10

pico p -12 10

Amount of substance mol e femto f -15 10

atto a -18 10

Add to 273.15 to Celsius scale scale to convert to kelvin scale To find the accurate value, we need to know the true value of a physical quantity. Nothing can be measured measured absolutely accurate. accurate. ...value close to the true value. Can be increase by sensitive instrument. Systematic: due to faulty apparatus Random: due to experimenter For sum Q=a+b For difference Q=a-b ΔQ=Δa+Δb ΔQ=Δa+Δb For product Q=a×b For division Q=a/b

K= θ oC +273.15

∆ = ∆ + ∆  × 

1.234 four sf

1.2 two sf

1002 four sf

3.07 three sf

0.001 one sf

∆ = ∆ + ∆  × 

0.012 two sf

0.0230 three sf

0.20 two sf

190 2 or 3 sf

the interval of confidence around the best measured value such that the measurement is certain not to lie outside this stated interval

 =    ±   × 100  =   =     ∆ ∆ = =  × 100  Scalar → only magnitude with units

Vector → magnitude with unit and direction eg. velocity, force etc

Eg. density, pressure, speed, speed, distance etc a and b same direction: apply simple addition a and b opposite direction: apply simple subtraction +  to each other: apply Pythagoras theorem =    Not to each other: apply cosine rule = + 2× × × 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  = tan tan  Not ⊥ to each other: use protractor x- component  =  × cos Time base: horizontal scale or x-axis

Important Equations for AS Physics Physics - 9702

y-component

 =  ×sin 

Vertical gain: vertical scale or y-axis

Prepared by Faisal Jaffer, Nov 2011

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2

Unit 2: Motion, force and energy (topic 3, 4, 5 and 6 from AS syllabus)

̅

1

Average velocity

2 3

Instantaneous Instantan eous velocity Average acceleration acceleration



s is the displacement in meters and t ̅ =  is the time in seconds. Velocity of an object at any particular instant of time. v is the change of speed and t is  = ∆ the change of time. Unit of ∆ acceleration is ms Δ

Δ

-2

4

Acceleration and velocity

5

Graphical representation representation

6

Speed-time graph

7 8

Distance-time Distance-t ime graph Equation for uniform motion, constant motion Equations for uniformly accelerated motion - body start motion u=0 - body come to rest v=0 -2 - free fall g=a=9.81ms - horizontal motion s=x - vertical motion s=h=y Friction → static and dynamic

9

10

11

12 13

14

Air resistance or viscous force or viscous drag Terminal velocity Projectile: Motion in two dimensions, dimensions, v and angle θ with horizontal, upward is +

15

Weight and mass: weight is force of gravity, mass is the amount of matter, it never changes Stability of an object

16

Momentum

Same direction: acceleration is +ve (if velocity is in +ve direction) Opposite direction: acceleration is -ve, deceleration, retardation

Area under the graph: distance covered by and object Gradient of the graph: acceleration Gradient of the graphs: speed of an object only use when acceleration=0 and = no net force is applied v is the final velocity in ms , = + -1 ( + ) u is the initial velocity in ms , = s is the distance/displacement distance/displacement in m, 2 -2 1  a is the acceleration in ms and = + t is the time in s. 2

            =  + 2 Static  =  ×  Dynamic  =  × 

f s is the static friction in newton, f k k is the dynamic friction in newton, µs is the coefficient of static friction N is the reaction or normal force µk is the coeff. of dynamic friction perpendicular to the surface - Opposing force to the motion in presence of air or fluid - During free fall in the beginning: weight air resistance+upthrust resistance+upthrust - Later: weight > resistance+upthrust - at terminal velocity, weight = air resistance + upthrust x-component → y-component → horizontal range  no acceleration acceleration is g



 =  cos   =   =  cos 

 =  ×

≫

 =  sin    =   − ½

 =  2 -2

due to gravity=9.81 ms

Lower the centre of gravity →more stable the object is Wider the base of an object →more stable the object is Momentum=mass×velocity Momentum=mass×velocity unit is kg.m.s or N.s

p=m×v

o

max range at θ=45 w is the weight in newton (N), m is the mass in kg and g is acceleration





3

20

Inelastic collision

Total kinetic energy before collision>total collision>total kinetic energy after collision

  + ½  > ½  + ½

½ 21 22

23 24

Object in motion → stay in motion forever object stationary → stay stationary forever unless force applied - Net force applied ⋉ acceleration  - Mass of an object ⋉ 1/acceleration 1 -1 N is the amount of force require  = -2 to create an acceleration of 1 ms of  = -1 -1 2 mass of 1 kg; k=1Nkg m s Newton’s third law of Action and reaction forces forces applied by two two objects on each other is always always motion equal in magnitude and opposite in direction Momentum and 2nd law of Rate of change of momentum momentum is = = motion equal to the net force applied Newton’s first law of motion Newton’s second law of motion

25 Impulse 26 Density ‘ρ’ in kgm or -3 gcm 27

Pressure p in pascal (Pa)

28

Pressure in fluids due to depth h in meters

29

Upthrust: - upward force applied by fluid on an object

30

Measuring the density of liquid using (upthrust) Archimedes principle 31 Torque or moment of force 32 Torque due to a couple or two equal forces 33 Conditions Condition s of equilibrium 34

35

35 36

Work : ΔW is the work in joules External work done by an expanding gas Work done in stretching stretch ing a spring Principal of conservation of mechanical energy

 ⋉  ⋉ ⁄    

  −   ∆ = −  = m is the mass and V is the volume  =   = ℎ ℎ = ℎ

* upthrust is equal to the weight of the liquid displaced

Constant force acting for short time - ρ of Mercury is 13.6gcm -3 o - ρ of water water is 1gcm at 4 C - ρ of air 0.001293gcm 0.001293gcm-3 F is the force in N and A is the area 2 on which the force applied in m ρ is the density of the fluid, g is the acceleration due to gravity and h is the height or depth in metre - Object floats if the density of object is less than or equal to the density of the fluid and object sinks if the density of object is more than the density of fluid

   = ℎ      ℎ   F applied perpendicular to d  =  ×sin  Couple = one force × perpendicular distance between the two forces

Σ = 0 Σ = 0 ∆ =  × cos

 = 

work that causes motion → E k k work that store energy →E p

∆ = ∆

In p-V graph the area under under the graph is the work done

-Total or net force applied is zero -Total torque applied is zero F is the force, s is the displacement in the direction of the force applied and θ is the angle between F and s p is the pressure in Pa Pa and ΔV is the 3 expansion of gas in m

∆ = ½ = ½

F is the force applied and x is the extension Work= area under the F-x graph Loss of gain or E p=gain or loss of E k k

Δ = Δ  ℎ = ½





4

38

39

Internal energy: Sum of the E k k and E p of the molecules of a system Power

40

Efficiency of a machine

∆ = ∆ + ∆

ΔQ

heat applied, ΔU increase in the internal energy and ΔW is the work done by the system P is the power in watts, W is the work done, F is the force and t time

 =  =    × 100  =    

Efficiency can be expressed as percentage





5

Unit 3: Electric charge (topic 17, 19 and 20 from the s yllabus)

1

Electric field intensity E: force on a unit charge q at any point around another charge Q

..between the two parallel plates

Current: Rate of flow of charges in a conductor

3 4

Current path Conduction of electric charge Ohms law

5

6

Voltage

7

Electromotive force(emf)

8

Max. Power dissipated dissipat ed by the cell

9

Resistance and resistivity

10

Circuit

11 12

Resistance in series Resistance in parallel

13

Potential divider

14 15

Potential divider (V total voltage) Power

16

Power

17

I-V Characteristics

 = 

.. decreases with distance increase, -1 unit is NC I is the current in amperes (A), (A), = Q is the charge in coulombs (C) t is the time in seconds (s) In circuits the current always choose the easiest path ..in electrolyte liquids due chemical reaction, ions → electrolysis ..in liquids (eg mercury) or solids (metals) due to free electrons → conduction Voltage across the resistor is V is the voltage in volts (V), directly proportional to current, I is the current in amperes (A) and R is resistance in ohms (Ω) V ⋉ ⋉ I or separation d, unit is Vm

2

..due to point point charge Q on charge charge q

 =  .. uniform between the plates -1

 

 =  Energy per unit charge  =  

e.m.f. = lost volts + terminal p.d. e.m.f.=Ir+IR unit of emf is volts (V)

   = ( + )   =   ρ is the resistivity of resistor in Ω.m

Q is the charge in coulombs (C), V is the voltage in volts (V) Energy is in joules (J) the energy transferred to electrical energy and when 1C charge passes through a circuit . Max. power P when R=r, E is the emf

R is the resistance a resistor, resistor, L is the length of a resistor resistor in meters A is the area of cross-section cross-section of a 2 resistor in m In series circuit → the current stays the same and voltage divides In parallel circuit → the voltage stays the same and current divides

 =  +  +  + ⋯ R, R , R and R are resistances of 1 1 1 1 resistor in ohms  =  +  +  + ⋯  =  V voltage across R V voltage across R    = ( +  ) ×   = ( +  ) ×   =  ×   =  ×   =  P is the power in watts (W) The unit of energy is joules (J)  =   metals diode filament thermistor LDR 1

I ↑, ↑, V↑

I in one direction

2

3

1

1

2

2

V ↑,T↑,R↑,I↓ ↑,T↑,R↑,I↓

T ↑, ↑, R↓, I↑

L↑,R↓.I↑





6

Unit 4: Matter (topic 9, and 10 from the syllabus)

1 2 3

Density: ratio of mass to -3 -3 volume, gcm , kgm Kinetic molecular theory of matter Kinetic molecular theory of matter energies

4 5

Brownian Motion Pressure, p

6

Pressure due to liquid

7

Kinetic energy of the particles of a substance substance Potential energy of the particles of a substance Types of solids (based on the arrangement of atoms or molecules)

8 9

10

Hooke’s Law

 = 

ρ=m/V where where m is the mass and V is the vol. tiny particles, in constant collision, held by strong electric force, large empty space, temp increases the speed of particles, particles, Solids: Liquids: Gases: vibrates at mean position vibrational energy and Vibrational, called vibrational energy translational (movement) translational and energy rotational energies Random, zigzag motion of particles Unit is pascal (Pa)

 ℎ      =      =  × ×ℎ

ρ is density, g is gravity and h is depth proportional to the the thermal energy of a substance substance

Due to electrostatic force force between particles of a substance Crystalline solids: Atoms or molecules are arranged arranged in regular three dimensional pattern

Polymer solids are either crystalline polymer if the molecules are arranged in some form of regular pattern or amorphous polymer if there is no particular systematic arrangement The extension of a spring Δ x is directly proportional proportional to the force applied applied F app app provide the elastic limit limit is not reached  = or



11

Elastic limit

12

Stress σ (unit pascal)

13

Strain ε (no unit)

14

Young modulus E (unit is pascal)

15

Young modulus E

16

Elastic Hysteresis loop

Non-crystalline or amorphous amorphous solids: Atoms or molecules are not not arranged in regular pattern

  = −

k is the spring constant and F s is the restoring force of spring Gradient or slope of the graph between force F (y-axis) (y-axis ) and extension x (xaxis) is the elastic limit of a spring F is the force applied and A is the  area of cross-section perpendicular perpendicular  =  to the force x is the change in length and and L is  =  the original length    ×  ratio of stress over strain   =  =  =  ×   Gradient or slope of the graph between stress  (y-axis) and strain  (x-axis)

is the Young modulus of a spring The difference between the areas covered by force- extension during the expansion to when it is returning back to its original shape is called elastic







7

18

Strain energy per unit volume

19

Ductile and brittle material

    1 = ×  ×  2 1 = × × 2

The area under the stress-strain graph is called strain energy per unit volume. The unit of energy is joules (J).

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

2 3 4

Nucleon no ‘A’ Proton no ‘Z’ Alpha particles α-particles

5

Beta-particles β -particles -particles

6

Gamma-particles γ-particles

7

Alpha decay

8

Beta decay

9

Gamma decay

10

Radioactivity is a spontaneous process Radioactivity is a

11

Proton: Electron: Neutron: Positive charge, negative charge, no charge, inside the nucleus, revolve around the nucleus, inside the nucleus, same mass as neutron mass is 1/1836 of proton same mass as proton also called mass number or atomic weight, it is sum of protons and neutrons also called atomic number, total number of protons  Helium nucleus Stopped by paper or  Highest ionization ionization potential Fast moving electrons  Stopped by aluminum or Less ionization potential potential  Electromagnetic radiation radiation  Only stopped by thick a sheet of lead Least ionization potential potential Parent nuclei X emit two protons and two    +  + neutrons to make alpha particle In parent nuclei X one of the the neutrons    changes into neutron and electron. The  +  + electron emits as beta Gamma decay is the simple loss of energy   +  from the nucleus Does not depend upon the environmental factors factors eg atm. Pressure, Pressure, temperature, humidity, brightness etc All the nuclei have equal probability probability of decay decay at any time, cannot predict predict

    

 ⇒     ⇒     ⇒  





8

Unit 5: Waves (topic 15 and 16 from the syllabus)

1

Wave equation 1

2

Wave equation 2

3

9 10

Movement of the particles of the medium Wavelength Frequency ‘f’ Time period ‘T’ Speed of wave motion ‘v’ Displacement of particle ‘s’ Amplitude ‘a’ Wave fronts

11 12

Progressive wave Phase difference differen ce

13 14

Coherent waves Intensity Intensit y of a wave ‘ I’

15

Intensity of a wave ‘I’

16 17 18 19

Compression Compress ion region Rarefaction Rarefacti on region Diffraction Diffract ion Interference of light waves

20

Young double slit

4 5 6 7 8

′′

 =  × 

-

v is the speed of wave in ms f is the frequency in Hz wavelength in metre λ is the wavelength 1 T is the time period of wave in = second Longitudinal waves=> waves=> back and forth same direction direction as waves waves Transverse waves=> perpendicular to the direction of waves Distance between two two crests or two troughs, unit metre (m) Total number of waves in one second, unit hertz (Hz) Time taken for one complete wave, unit second (s) Distance move by crest in direction of wave in 1second, unit ms Distance move by a particle from its mean position position in either direction, unit metre (m) The maximum distance move by the particle, unit metre (m) Representation Represent ation of crests of a wave by straight straigh t line perpendicular perpendicula r to the direction of wave. Distance between two wave fronts is wavelength. Continuous waves created by a source When the crests and troughs of two waves do not overlap each other then two waves have phase difference Two waves of same properties and originate from same source P the amount of wave energy = per second at particular particular point -2 Unit of intensity is Wm falling on surface area area A Intensity of wave is directly proportional to the amplitude square

 

 

 ⋉ 

When particles of a medium come close to each other Where particles of a medium move further apart from each other When waves pass through a narrow gap, they spread out. Constructive interference: Destructive interference: interference: When the crests-crests and When crests-troughs of two troughs-troughs of two waves waves overlap each other, overlap each other, amplitudes amplitudes cancel each other become added For bright fringes:

For dark fringes:





9

24

Stationary waves in a string of length ‘L’ and speed of wave is ‘v’

Fundamental Fundamental mode or first harmonic:

 = 

or

(one loop) 25

Stationary waves in a string of length ‘L’

26

Stationary Stationa ry wave in an air column one end open one end close

 =   

(two loops)

Fundamental Fundamental mode or first harmonic: or

(½ loop)





Second overtone or third harmonic:

 =  or   = 

(three loops) For nth harmonic frequency:   = where n= 1, 2, 3,....

  = 

First overtone or second harmonic:  or  = =



First overtone or second harmonic:

Second overtone or third harmonic:

 =   =   or  =   =  or   =  (1 ½ loops)

(1 ½ loops)

For nth harmonic frequency:

  =   where n=1,2,3. (

27 28 29

)

Speed Speed of light light In air: 3×10 3×10 m/s In glass: glass: 2×10 m/s In water: water: 2.25×10 2.25×10 m/s Electromagnetic Spectrum:→ this way the frequency decreases and wavelength increases Gamma rays ↔ X -rays -rays ↔ UV ↔ Visible light ↔ IR ↔ Micro waves ↔ Radio waves

Important Equations in Physics As

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