Important Equations in Physics for IGCSE course General Physics: 1 For constant motion: π£= π π‘ 2 For acceleration ‘a’ 3 Graph π£−π’ π‘ Area of a rectangular shaped graph = base × height. π= ‘v’ is the velocity in m/s, ‘s’ is the distance or displacement in meters and ‘t’ is the time in seconds u is the initial velocity, v is the final velocity and t is the time. In velocity-time graph the area under the graph is the total distance covered by an object. Area of triangular shaped graph = ½ × base × height 4 Weight and mass π€ =π×π 5 Density ‘ρ’ in kg/m3 6 Force F in newton (N) 7 8 Terminal Velocity Hooke’s Law 9 Moment of a force in N.m 10 Law of moment or equilibrium: π= π πΉ =π×π m is the mass and a is the acceleration Wπiπβπ‘ πƒ ππ ππjπππ‘(πππ€ππ€πππ) = πiπ πππ iπ π‘ππππ (π’ππ€ππππ ) F is the force, x is the extension in meters and k is the spring πΉ =π×π₯ constant. F is the force and d is the ππππππ‘ πƒ ƒππππ = πΉ × π distance from the pivot πππ‘ππ ππππππ€iπ π ππππππ‘ = π‘ππ‘ππ πππ‘iππππππ€iπ π ππππππ‘ => πΉ1 × π1 = πΉ2 × π2 W =πΉ×π 11 Work done W joules (J) 12 Kinetic Energy Ek in joules (J) 13 Potential Energy Ep in joules (J) 14 Law of conservation of energy: 15 Power in watts (W) 16 Pressure p in pascal (Pa) 17 Pressure p due to liquid 18 Atmospheric pressure Prepared by Faisal Jaffer π w is the weight in newton (N), m is the mass in kg and g is acceleration due to gravity = 10 m/s2 m is the mass and V is the volume πΈ = π 1 × π × π£2 2 πΈπ = π × π × β F is the force and d is the distance covered by an object m is the mass(kg) and v is the velocity (m/s) m is the mass (kg) and g is the acceleration due to gravity and h is the height from the ground. πΏππ π πƒ πΈπ = ππiπ πƒ πΈπ 1 π × π × β = × π × π£2 2 π€πππ ππππ π‘iππ π‘ππππ πΈπππππ¦ π‘ππππ ƒππ π= π‘iππ π‘ππππ πΉ π= π΄ π= Power is the rate of doing work F is the force in newton(N) and A is the area in m2 ρ is the density in kg/m3, g is the acceleration due to garvity and h π=π×π×β is the height or depth of liquid in meters. P=760mmHg = 76cm Hg =1.01x105Pa Page 1 Thermal Physics: 1 2 Pressure and volume relationship (Boyle’s law) Thermal Expansion (Linear) 3 Thermal Expansion (Cubical) 4 5 Relationship between linear and cubical expansivities Charle’s Law: Volume is directly proportional to absolute temperature ππΊπ Pressure Law: Pressure of a gas is directly proportional to the absolute temperature ππΊπ 7 Gas Law: ππ = ππππ π‘πππ‘ π 8 Specific Heat Capacity: The amount of heat required to raise the temperature of 1 kg mass by 1oC. 9 Thermal Capacity: amount of heat require to raise the temperature of a substance of any mass by 1oC 10 Specific latent heat of fusion (from Ice to liquid) 6 11 Specific latent heat of vaporization (from liquid to vapour) 12 Thermal or heat transfer 13 Emitters and Radiators Prepared by Faisal Jaffer pV=constant p1 and p2 are the two pressures in Pa π1 × π1 = π2 × π2 and V1 and V2 are the two volumes in m3 ΔL = α ×Lo ×Δθ Lo is the original length in meters, Δθ is the change in temperature in oC, ΔL is the change in length in meters (L1- Lo) and α is the linear expansivity of the material οV = ο§ Vo οο±ο Vo is the original volume in m3, Δθ is the change in temperature in oC, ΔV is the change in volume in m3 (V1- Vo) and ο§ is the cubical expansivity of the material. ο§ = 3ο‘ο π V is the volume in m3 and T is the temperature in Kelvin (K). = ππππ π‘πππ‘ π π1 π 2 = π1 π2 π p is the pressure in Pa and T is the temperature in Kelvin (K). = ππππ π‘πππ‘ π π π2 1 = π1 π2 π1π 1 π2 π 2 = π1 π2 π π= π × βπ Thermal capacity=m×c πβπππππ πππππiπ‘π¦ = πΏ = ƒ πΏ = π£ π π π π π In thermal physics the symbol θ is used of celsius scale and T is used for Kelvin scale. c is the specific heat capacity in J/kgoC, Q is the total heat in joules (J), m is the mass in kg and Δθ is the change in temperature The unit of thermal capacity is J/oC. βπ Lf is the specific latent heat of fusion in J/kg or J/g, Q is the total heat in joules (J), m is the mass of liquid change from ice in kg or g. Lv is the specific latent heat of vaporization in J/kg or J/g, Q is the total heat in joules (J), m is the mass of vapour change from liquid in kg or g. In solid = conduction In liquid and gas = convection and also convection current In vacuum = radiation Dull black surface = good emitter, good radiator, bad reflector Bright shiny surface = poor emitter, poor radiator, good reflector Page 2 Waves, light and sound: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Wave equation 1 π£ =ƒ×π v is the speed of wave in m/s f is the frequency in Hz λ is the wavelength in meters 1 Wave equation 2 T is the time period of wave in ƒ= seconds π Movement of the particles Longitudinal waves=> back and forth in the direction of the of the medium waves Transverse waves=> perpendicular to the direction of the waves Law of reflection Angle of incidence i = angel of reflection πππππ iπ = πππππ ππ Refraction From lighter to denser medium → light bend towards the normal From denser to lighter medium →light bend away from the normal Refractive index n π iπ ∠i Refractive index has no unit π = π iπ ∠π Refractive index n π ππππ πƒ πiπβπ‘ iπ πiπ ππ π£πππ’π’π π= π ππππ πƒ πiπβπ‘ iπ πππ¦ ππ‘βππ πππiπ’π Image from a plane mirror Virtual, upright, same size and laterally inverted, same distance from the mirror inside Image from a convex lens When close: virtual, enlarge, upright When far: real, small, upside down Image from a concave lens Virtual, upright, small Critical angle When light goes from denser to lighter medium, the incident angle at which the reflected angle is 90o,is called critical angle. Total internal When light goes from denser to lighter medium, the refracted ray reflection(TIR) bend inside the same medium then this is called (TIR) Electromagnetic Spectrum:→ this way the frequency decreases and wavelength increases Gamma rays ↔ X-rays ↔ UV ↔ Visible light ↔ IR ↔ Micro waves ↔ Radio waves Colours of visible VIBGYOR (from bottom-up) spectrum (light) Speed of light In air: 3×108m/s In glass: 2×108m/s Light wave Electromagnetic waves longitudinal waves Sound wave particle of the medium come close → compression particles of the medium far apart → rarefaction Echo 2×π v is the speed of sound waves, π£= d is the distance in meters π‘ between source and the reflection surface and t is the time for echo Properties of sound waves Pitch means the frequency of the wave Loudness means the amplitude of the wave Speed of sound waves Air : 330-340 m/s Water: 1400 m/s Concrete : 5000 m/s Steel: 6000 – 7000 m/s Prepared by Faisal Jaffer Page 3 Electricity and magnetism: 1 Ferrous Materials 2 Non-ferrous materials 3 Electric field intensity 4 Current: Rate of flow of charges in a conductor 5 6 Current Ohms law 7 Voltage 8 9 E.M.F. Electromotive force Resistance and resistivity 10 Circuit 11 12 Resistance in series Resistance in parallel 13 Potential divider 14 Potential divider 15 Power 16 Power 17 Transformer 18 Transformer 19 Cathode rays Attracted by magnet and can be magnetized Not attracted by magnet and cannot be magnetized force exerted by the field on a unit charge placed at a point around another charge Eg. iron, steel, nickel and cobalt copper, silver, aluminum, wood, glass E is the electric field intensity in N/C πΉ πΈ= π π I is the current in amperes (A), Q is the charge in coulombs (C) π‘ t is the time in seconds (s) In circuits the current always choose the easiest path V is the voltage in volts (V), Voltage across the resistor is directly proportional to current, I is the current in amperes (A) and R is resistance in ohms (Ω) VοΏ½ I or π =π πΌ Energy per unit charge Q is the charge in coulombs (C), πΈπππππ¦ V is the voltage in volts (V) π= Energy is in joules (J) π e.m.f. = lost volts + terminal potential difference EMF=Ir+IR πΏ R is the resistance a resistor, π =π L is the length of a resistor in meters π΄ ρ is the resistivity of resistor in Ω.m A is the area of cross-section of a resistor in m2 In series circuit→ the current stays the same and voltage divides In parallel circuit → the voltage stays the same and current divides π = π 1 + π 2 + π 3 R, R1, R2 and R3 are resistances of 1 1 1 1 = + + resistor in ohms π π 1 π 2 π 3 π 1 π 1 = π2 π 2 π 2 π 1 π2 = ( )×π π1 = ( )×π π 1 + π 2 π 1 + π 2 π2 P is the power in watts (W) π = πΌ × π π = πΌ2 × π π= π The unit of energy is joules (J) πΈπππππ¦ π = π‘iππ ππ π π Vp is the voltage in primary coil, = Vs is the voltage in secondary coil π π ππ np is the no of turns in primary and ns is the no of turns in secondary Power of primary coil = power of secondary coil ππ = ππ πΌπ × ππ = πΌπ × ππ π π πΌπ = ππ πΌπ Ip is the current in primary coil and Is the current in secondary coil Stream of electrons emitted from heated metal (cathode). This process is called thermionic emission. πΌ= 20 Prepared by Faisal Jaffer Page 4 Atomic Physics: 1 Alpha particles α-particles 2 Beta-particles β-particles 3 Gamma-particles γ-rays 4 5 Half-life Atomic symbol 6 Isotopes Prepared by Faisal Jaffer Helium nucleus Stopped by paper Highest ionization potential Fast moving electrons Stopped by aluminum Less ionization potential Electromagnetic radiation Only stopped by thick a sheet of lead Least ionization potential Time in which the activity or mass becomes half π΄ ZX A is the total no of protons and neutrons Z is the total no of protons Same number of protons but different number of neutrons Page 5
