Physics Summary

Typed version of the handwritten O Level Physics revision summary. The original handwritten pages are on the same page of megalecture.com.

Measurements

Quantity	SI unit	Quantity	SI unit
Mass	kg	Current	A
Length	m	Temperature	K
Time	s	Amount of substance	mol

Prefix	Value	Prefix	Value
nano (n)	10−9	deci (d)	10−1
micro (µ)	10−6	kilo (k)	103
milli (m)	10−3	mega (M)	106
centi (c)	10−2	giga (G)	109

If the vectors to be added are drawn clockwise, the resultant vector must be anticlockwise, or vice versa.

Kinematics

• speed = distance / time
• acceleration = velocity / time, the slope of a velocity–time graph. Velocity is the slope of a displacement–time graph.
• Terminal velocity: air resistance = weight, acceleration = 0, so the object travels at constant velocity (the velocity–time graph rises steeply, then levels off).

Dynamics

• Newton's first law: an object will stay at rest or in constant motion until a force acts on it.
• Newton's second law: force = mass × acceleration.
• Newton's third law: every action has an equal and opposite reaction.
• Balanced forces allow an object to stay at rest or in constant motion; unbalanced forces will cause it to accelerate or decelerate.
• The resultant force is zero when an object is travelling at constant speed.

Mass, weight and density

• mass = force / acceleration = density × volume = weight / g.f.s.
• weight (N) = mass × gravitational field strength
• density (g/cm³) = mass / volume

Turning effect of forces

• moment of force = force × distance
• Principle of moments: F₁ × d₁ = F₂ × d₂

Deformation

force = spring constant × extension (or compression)

Pressure

• pressure = force / area
• pressure in liquids = ρgh = density × g.f.s. × depth of liquid
• Pascal's principle: F_x / A_x = F_y / A_y
• Boyle's law: P₁V₁ = P₂V₂

Energy sources and transfer of thermal energy

• work done (J) = force × distance (energy is the ability to do work)
• power = work done / time (the rate of doing work)
• kinetic energy = ½mv² (mass in kg, velocity in m/s)
• gravitational potential energy = mgh
• E = mc² (energy; c = speed of light = 3 × 10⁸ m/s)
• efficiency = (energy or power output / energy or power input) × 100
• elastic potential energy = ½ke²

Temperature

θ = (L_θ − L₀) / (L₁₀₀ − L₀) × 100, where L₀ is the length of mercury at the ice point, L₁₀₀ the length at the steam point and L_θ the length at the unknown temperature.

sensitivity = increase in mercury level / increase in temperature (Δl / Δθ)

Thermal properties of matter

• heat capacity (J/K or J/°C) = Q / θ, where Q is the energy supplied and θ the increase in temperature: the heat energy required to raise the temperature of a substance by 1 °C.
• specific heat capacity (J/(kg K) or J/(kg °C)) = Q / (mθ), where m is the mass of the substance: the heat energy required to raise the temperature of 1 kg of a substance by 1 °C.
• Q = ml, with l the latent heat (J/kg) and m the mass of substance that has changed state.

General wave properties

• velocity = frequency × wavelength: v = fλ (λ is "lambda")
• frequency = 1 / T

Light

• refractive index n = sin i / sin r = c / v (speed of light in a vacuum / speed of light in the medium) = real depth / apparent depth
• critical angle: C = sin⁻¹(1 / n)

Electromagnetic spectrum

Wave	Typical frequency (Hz)	Uses
Radio waves	104	television, radio
Microwaves	1010	satellites
Infra-red	1013	remote-control devices, grills and toasters
Visible light	1014	optic fibres for transmission of signals (and fluorescent tubes)
UV rays	1015	sun-beds, sterilising medical equipment
X-rays	1017	2-dimensional images in medicine, scanners
Gamma rays	1020	killing cancerous cells and tumours, finding cracks in metals

Sound

• Higher pitch = higher frequency; larger amplitude = louder.
• Speed of sound: solid > liquid > gas. Speed of sound in air ≈ 330 m/s.

Electromagnetism

• Right-hand grip rule gives the direction of the field around a current.
• ⊙ = current out of the page; ⊗ = current into the page.
• Two wires carrying current in the same direction attract each other; in opposite directions they repel.
• Fleming's left-hand rule: first finger = magnetic field, thumb = force, second finger = direction of current.
• Split-ring commutators are used in d.c. motors; slip rings in a.c. generators.

Current electricity

• current (amperes) = charge / time; 1 A = 1 C / 1 s
• voltage (volts) = energy / charge = work done / charge; 1 V = 1 J / 1 C
• V = IR; resistance (ohms) = voltage / current
• V–I and I–V graphs: filament lamp (curve bending over), thermistor (curve bending up), diode (no current until a forward voltage, then a straight rise).
• Series resistors: I₁ = I₂ = I₃; V = V₁ + V₂ + V₃; R = R₁ + R₂ + R₃
• Parallel resistors: I = I₁ + I₂ + I₃; V₁ = V₂ = V₃; 1/R = 1/R₁ + 1/R₂ + 1/R₃
• E = Pt = IVt = I²Rt (joules); power = VI (watts)
• e.m.f. and p.d. are both voltages. Cells in series: E = E₁ + E₂ + E₃. Cells in parallel: E₁ = E₂ = E₃; if one fails the others keep working, they last longer, lower resistance, less energy loss.
• Energy = power × time: joules = watts × seconds; kilowatt-hours = kilowatts × hours.

Electronics

Potential divider: V₁ = (R₁ / (R₁ + R₂)) × V, and V₂ = (R₂ / (R₁ + R₂)) × V, where V is the supply across R₁ and R₂ in series and V₁, V₂ are the voltages across each.

Radioactivity

Unstable nuclei emit:

• α particles (helium nuclei, ⁴₂α): higher mass, so greatest ionisation power and least penetration; stopped by paper or 8–10 cm of air; speed about 10% of c; deflected (less) in electric and magnetic fields.
• β particles (electrons, ⁰₋₁β): ionisation power less than α, penetration greater than α; stopped by a few mm of aluminium; speed about 90% of c; deflected most in electric and magnetic fields.
• γ rays (electromagnetic waves): no charge, no mass; greatest penetration, stopped by a lead block; least ionisation; not deflected because they carry no charge; c = 3 × 10⁸ m/s.

• ^A_ZX → ⁴₂α + ^A−4_Z−2Y
• ^A_ZX → ⁰₋₁β + ^A_Z+1Y
• ^A_ZX → γ + ^A_ZX

In every half-life, the number of atoms, the mass and the activity halve.

Still to add (from the last page's to-do list): the vertical-row / horizontal-line notation, melting point, boiling point, scale, periscope image properties, and a comparison of distance–time and speed–time graphs.