Igcse Physics Formulas

Speed

𝘃 = d ÷ 𝘁

v = speed [m/s]

s = distance [m]

t = time [s]

Acceleration

𝗮 = (𝘃 − 𝘂) ÷ 𝘁

a = acceleration [m/s²]

v = final velocity [m/s]

u = initial velocity [m/s]

t = time taken [s]

Distance (speed–time graph)

𝗱𝗶𝘀𝘁𝗮𝗻𝗰𝗲 = 𝗮𝗿𝗲𝗮 𝘂𝗻𝗱𝗲𝗿 𝘁𝗵𝗲 𝘀𝗽𝗲𝗲𝗱–𝘁𝗶𝗺𝗲 𝗴𝗿𝗮𝗽𝗵

• distance [m]

• speed [m/s]

• time [s]

Acceleration (speed–time graph)

𝗮𝗰𝗰𝗲𝗹𝗲𝗿𝗮𝘁𝗶𝗼𝗻 = 𝗴𝗿𝗮𝗱𝗶𝗲𝗻𝘁 𝗼𝗳 𝘁𝗵𝗲 𝘀𝗽𝗲𝗲𝗱–𝘁𝗶𝗺𝗲 𝗴𝗿𝗮𝗽𝗵

• acceleration [m/s²]

• speed [m/s]

• time [s]

Force (Newton’s second law)

𝗙 = 𝗺 × 𝗮

• F = resultant force [N]

• m = mass [kg]

• a = acceleration [m/s²]

Weight

𝗪 = 𝗺 × 𝗴

• W = weight [N]

• m = mass [kg]

• g = gravitational field strength [N/kg (9.8)]

Gravitational field strength

𝗴 = 𝗪 ÷ 𝗺

• g = gravitational field strength [N/kg (= m/s²)]

• W = weight [N]

• m = mass [kg]

Density

𝞀 = 𝗺 ÷ 𝗩

• ρ = density [kg/m³ or g/cm³]

• m = mass [kg or g]

• V = volume [m³ or cm³]

Volume of an irregular solid (displacement)

𝗩 = 𝗩₂ − 𝗩₁

• V = volume of solid [cm³]

• V₂ = final water level [cm³]

• V₁ = initial water level [cm³]

Pressure

𝗽 = 𝗙 ÷ 𝗔

• p = pressure [Pa (= N/m²)]

• F = force [N]

• A = area [m²]

Pressure change in a liquid

𝝙𝗽 = 𝞀 × 𝗴 × 𝝙𝗵

• Δp = change in pressure [Pa]

• ρ = liquid density [kg/m³]

• g = gravitational field strength [N/kg]

• Δh = change in depth [m]

Moment of a force

𝗠 = 𝗙 × 𝗱

• M = moment [N m]

• F = force [N]

• d = perpendicular distance from the pivot [m]

Principle of moments (balanced)

𝗙₁ × 𝗱₁ = 𝗙₂ × 𝗱₂ (𝗰𝗹𝗼𝗰𝗸𝘄𝗶𝘀𝗲 𝗺𝗼𝗺𝗲𝗻𝘁 = 𝗮𝗻𝘁𝗶𝗰𝗹𝗼𝗰𝗸𝘄𝗶𝘀𝗲 𝗺𝗼𝗺𝗲𝗻𝘁)

• F = force [N]

• d = perpendicular distance from the pivot [m]

Spring force (Hooke’s law)

𝗙 = 𝗸 × 𝘅

• F = force [N]

• k = spring constant [N/m]

• x = extension [m]

Momentum

momentum = 𝗺 × 𝘃

• momentum [kg m/s]

• m = mass [kg]

• v = velocity [m/s]

Momentum in a collision (conservation)

𝗺₁𝘂₁ + 𝗺₂𝘂₂ = 𝗺₁𝘃₁ + 𝗺₂𝘃₂ = Momentum before = after

• m = mass [kg]

• u = velocity before [m/s]

• v = velocity after [m/s]

Impulse

𝗶𝗺𝗽𝘂𝗹𝘀𝗲 = 𝗙 × 𝝙𝘁 = 𝝙(𝗺𝘃)

• impulse [N S]

• F = force [N]

• Δt = time the force acts [s]

• Δ(mv) = change in momentum [kg m/s]

Work done

𝗪 = 𝗙 × 𝗱

• W = work done [J (= N m)]

• F = force [N]

• d = distance moved in the direction of the force [m]

Kinetic energy

𝗘ₖ = ½ × 𝗺 × 𝘃²

• Eₖ = kinetic energy [J]

• m = mass [kg]

• v = speed [m/s]

Gravitational potential energy

𝝙𝗘ₚ = 𝗺 × 𝗴 × 𝝙𝗵

• ΔEₚ = change in gravitational potential energy [J]

• m = mass [kg]

• g = gravitational field strength [N/kg]

• Δh = change in height [m]

Power (work or energy ÷ time)

𝗣 = 𝗪 ÷ 𝘁

• P = power [W (= J/s)]

• W = work done [J]

• ΔE = energy transferred [J]

• t = time [s]

Efficiency

𝗲𝗳𝗳𝗶𝗰𝗶𝗲𝗻𝗰𝘆 = (𝘂𝘀𝗲𝗳𝘂𝗹 𝗲𝗻𝗲𝗿𝗴𝘆 𝗼𝘂𝘁𝗽𝘂𝘁 ÷ 𝘁𝗼𝘁𝗮𝗹 𝗲𝗻𝗲𝗿𝗴𝘆 𝗶𝗻𝗽𝘂𝘁) × 𝟭𝟬𝟬%

• efficiency [%]

• energy [J (the power version uses W)]

Current (from charge)

𝗜 = 𝗤 ÷ 𝘁

• I = current [A]

• Q = charge [C]

• t = time [s]

Potential difference (p.d.)

𝗩 = 𝗪 ÷ 𝗤

• V = potential difference [V (= J/C)]

• W = work done (energy transferred) [J]

• Q = charge [C]

Electromotive force (e.m.f.)

𝗘 = 𝗪 ÷ 𝗤

• E = e.m.f. [V]

• W = work done by the source [J]

• Q = charge [C]

Resistance

𝗥 = 𝗩 ÷ 𝗜

• R = resistance [Ω]

• V = potential difference [V]

• I = current [A]

Electrical power

𝗣 = 𝗜 × 𝗩

• P = power [W]

• I = current [A]

• V = potential difference [V]

Electrical energy

𝗘 = 𝗣 × 𝘁

note: P = I x V

• E = energy transferred [J]

• P = power [W]

• t = time [s]

Energy in kW h

𝗲𝗻𝗲𝗿𝗴𝘆 (𝗸𝗪 𝗵) = 𝗽𝗼𝘄𝗲𝗿 (𝗸𝗪) × 𝘁𝗶𝗺𝗲 (𝗵)

• energy [KWH)]

• power [kW]

• time [h]

Cost of electricity

𝗰𝗼𝘀𝘁 = 𝗲𝗻𝗲𝗿𝗴𝘆 (𝗸𝗪 𝗵) × 𝗽𝗿𝗶𝗰𝗲 𝗽𝗲𝗿 𝗸𝗪 𝗵

• cost [$ (or other currency)]

• energy [kW h]

• price [$ per kW h]

Current in a series circuit

Current is Same everywhere

p.d. in a series circuit

Voltage Split up by each component

Total resistance in series

Resistance adds from each component

p.d. in a parallel circuit

Voltage stays the same across each branch

Current in each parallel branch

It splits up among the branches.

Use Ohm's Law with the total voltage and that branch's resistance: to find how much in eahc branch

Total current in a parallel circuit

Total current = current of each branch added

Total resistance in parallel

Total resistance actually decreases every time you add a resistor.

Potential divider (output p.d.)

• Vout = p.d. across R₂ [V]

• Vin = supply p.d. [V]

• R₁, R₂ = resistances [Ω]

Transformer: voltage and turns

• Vₚ, Vₛ = primary and secondary p.d. [V]

• Nₚ, Nₛ = primary and secondary turns [no unit]

Transformer: power in = power out

𝗩ₚ × 𝗜ₚ = 𝗩ₛ × 𝗜ₛ

• V = p.d. [V]

• I = current [A]

Power loss in cables

𝗣 = 𝗜² × 𝗥

• P = power wasted as heat [W]

• I = current in the cables [A]

• R = resistance of the cables [Ω]

Thermal energy (specific heat capacity)

𝝙𝗘 = 𝗺 × 𝗰 × 𝝙𝝷

• ΔE = energy transferred [J]

• m = mass [kg (or g, to match c)]

• c = specific heat capacity [J/(kg °C) or J/(g °C)]

• Δθ = temperature change [°C]

Temperature in kelvin

𝗧 = Celsius+ 𝟮𝟳𝟯

• T = temperature [K]

• Celsius = temperature [°C]

Gas pressure and volume (Boyle’s law)

𝗽₁ × 𝗩₁ = 𝗽₂ × 𝗩₂

(𝗳𝗶𝘅𝗲𝗱 𝗺𝗮𝘀𝘀, 𝗰𝗼𝗻𝘀𝘁𝗮𝗻𝘁 𝘁𝗲𝗺𝗽𝗲𝗿𝗮𝘁𝘂𝗿𝗲)

• Inversely Proportional

• p = gas pressure [Pa (same unit both sides)]

• V = gas volume [m³ (same unit both sides)]

Wave speed

𝘃 = 𝗳 × 𝝺

• v = wave speed [m/s]

• f = frequency [Hz]

• λ = wavelength [m]

Frequency (from period)

𝗳 = 𝟭 ÷ 𝗧

• f = frequency [Hz]

• T = period [s]

Period of an oscillation (practical)

𝗧 = 𝘁𝗼𝘁𝗮𝗹 𝘁𝗶𝗺𝗲 ÷ 𝗻𝘂𝗺𝗯𝗲𝗿 𝗼𝗳 𝗼𝘀𝗰𝗶𝗹𝗹𝗮𝘁𝗶𝗼𝗻𝘀

• T = period [s]

• total time [s]

Speed of sound (echo)

𝘃 = 𝟮𝗱 ÷ 𝘁

• v = speed of sound [m/s]

• d = one-way distance to the reflector

• [m] t = time for the echo [s]

Speed of light and EM waves

𝗰 = 𝗳 × 𝝺

• c = speed of light in a vacuum [m/s]

• f = frequency [Hz]

• λ = wavelength [m]

Refractive index (from angles)

𝗻 = 𝘀𝗶𝗻 𝗶 ÷ 𝘀𝗶𝗻 𝗿

• n = refractive index [no unit]

• i = angle of incidence [°]

• r = angle of refraction [°]

Refractive index (from speeds)

𝗻 = 𝗰 ÷ 𝘃

• n = refractive index [no unit]

• c = speed of light in a vacuum [m/s]

• v = speed of light in the material [m/s]

Critical angle

𝘀𝗶𝗻 𝗰 = 𝟭 ÷ 𝗻

• c = critical angle [°]

• n = refractive index [no unit]

Nucleon number

𝗔 = 𝗭 + 𝗡

• A = nucleon number [no unit]

• Z = proton number [no unit]

• N = neutron number [no unit]

Half-life (amount remaining)

$$P\left(1-\frac{50}{100}\right)^{n}$$

Alpha decay (nuclear equation)

𝗫(𝗔, 𝗭) → 𝗬(𝗔 − 𝟰, 𝗭 − 𝟮) + 𝗛𝗲(𝟰, 𝟮)

A = nucleon number [no unit] Z = proton number [no unit]

Beta decay (nuclear equation)

𝗫(𝗔, 𝗭) → 𝗬(𝗔, 𝗭 + 𝟭) + 𝗲(𝟬, −𝟭)

A = nucleon number [no unit] Z = proton number [no unit]

Orbital speed

𝘃 = 𝟮 𝝿 𝗿 ÷ 𝗧

• v = orbital speed [m/s]

• r = orbital radius [m]

• T = orbital period [s]

Hubble constant

𝗛₀ = 𝘃 ÷ 𝗱

H₀ = Hubble constant [per second)]

v = recession speed [m/s]

d = distance from Earth [m]

Age of the Universe

𝘁 ≈ 𝟭 ÷ 𝗛₀

t = age of the Universe [s (÷ 3.15 × 10⁷ for years)] H₀ = Hubble constant [s⁻¹]

Distance light travels

𝗱 = 𝗰 × 𝘁

d = distance [m]

c = speed of light [3.0 × 10⁸ m/s]

t = time

Power: in terms of energy

Power = 𝝙𝗘 ÷ 𝘁

• 𝝙𝗘 = energy transferred

• 𝘁 = time taken

work done relationship to energy transferred

Work Done = Energy Transferred

speed of light

$$3X10^8$$