Physics 5054 — chapter handouts

Speed, velocity and acceleration are three different things

Speed is how fast. Velocity is how fast and in which direction. Acceleration is how quickly the velocity changes. Because velocity includes direction, going round a bend at a steady speed still counts as accelerating — your direction is changing even though the speedometer is not.

A graph is a shortcut

On a distance–time graph, the steepness is the speed. On a speed–time graph, the steepness is the acceleration and the area underneath is the distance travelled. That area trick turns a nasty calculation into a triangle and a rectangle, and it appears in the exam every year.

Balanced forces mean no change

A car at a steady 60 km/h has a big engine force forward and an equally big drag force backward. They cancel, so the resultant force is zero, so it does not speed up or slow down. Force is not what keeps it moving — force is what would change its motion.

Falling: why a skydiver stops speeding up

As you fall faster, air resistance grows. Eventually air resistance equals your weight, the resultant force becomes zero, and you stop accelerating. You keep falling — fast — but at a constant terminal velocity.

Energy is never made or lost

It only changes form. A ball on a shelf has gravitational potential energy; drop it and that becomes kinetic energy; it lands and becomes sound and heat. Add up the total before and after and you get the same number, every time.

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Everything is made of moving particles

In a solid the particles vibrate in fixed positions. In a liquid they are still touching but can slide past each other. In a gas they are far apart and fly around freely. Almost every fact in this topic follows from that one picture.

Heating makes things bigger

Warm the particles and they vibrate more, so they need more room — the object expands. That is why bridges have expansion gaps, why railway lines used to buckle in heatwaves, and why a tight metal jar lid loosens under hot water.

Three ways heat travels

Conduction: particles jostle their neighbours — needs contact, works best in metals because free electrons carry energy fast. Convection: hot fluid becomes less dense, rises, and cooler fluid sinks to replace it — only in liquids and gases. Radiation: infrared waves, needs no material at all, which is how the Sun's energy crosses empty space.

Changing state costs energy but no temperature

Heat ice at 0 °C and the temperature refuses to rise until every last bit has melted. The energy is going into breaking the bonds holding the solid together, not into making particles faster. That is why ice is so good at keeping a drink cold.

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Two types, one difference

In a transverse wave the wobble is at right angles to the direction of travel — light, and waves on a rope. In a longitudinal wave the wobble is along the direction of travel, squashing and stretching as it goes — that is sound. Sound needs a material to squash, which is exactly why space is silent.

The one equation you use constantly

Speed = frequency × wavelength. Frequency is how many waves go past each second; wavelength is how long one wave is. Multiply them and you get how far the wave travels each second.

Waves bend, bounce and spread

Reflection bounces a wave off a surface — the angle in equals the angle out. Refraction bends a wave when it changes speed entering a new material, which is why a straw looks broken in a glass of water. Diffraction spreads a wave out through a gap, and it spreads most when the gap is about the size of the wavelength.

Light: the whole family

Radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Same family, same speed in a vacuum, differing only in wavelength and frequency. The shorter the wavelength, the more energy each bit carries — which is why gamma rays are dangerous and radio waves are not.

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The circuit must be a complete loop

Charge does not get used up. The same current flows out of a battery as flows back into it. What gets used up is energy, which the charges hand over as they pass through components. A bulb does not consume current; it consumes energy.

Series and parallel behave differently

In series there is one path, so the current is the same everywhere and the voltage is shared out between components. In parallel there are branches, so each branch gets the full voltage and the current splits between them. House wiring is parallel — which is why one blown bulb does not darken the house.

V = IR ties it together

Voltage equals current times resistance. Push harder (more voltage) and more current flows. Add resistance and less current flows. Almost every calculation in this topic is this equation rearranged.

Electricity and magnetism are the same story

A current creates a magnetic field around it — that is an electromagnet, and it is how motors, relays and doorbells work. Run it backwards: move a magnet near a wire and you generate a current. That is how essentially all the world's electricity is made, in power stations spinning magnets near coils.

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Inside the atom

A tiny nucleus of protons and neutrons, with electrons far outside. The nucleus is minute — if an atom were a football stadium, the nucleus would be a pea on the centre spot, and the rest is empty space. That is exactly what the alpha-scattering experiment showed: most particles sailed through, a few bounced back off something small and dense.

Three kinds of radiation

Alpha is a helium nucleus — heavy, strongly ionising, stopped by a sheet of paper. Beta is a fast electron — stopped by a few millimetres of aluminium. Gamma is a high-energy wave — reduced by thick lead but never fully stopped. The rule: the more strongly something ionises, the faster it runs out of energy, so the less far it travels.

Half-life is a fixed property

The half-life is the time for half the undecayed nuclei to decay. After one half-life, half remain; after two, a quarter; after three, an eighth. Nothing changes it — not heat, not pressure, not chemistry. You cannot speed radioactive decay up or slow it down.

Useful and dangerous, for the same reason

Radiation ionises — it knocks electrons off atoms. That is why it damages living cells, and also why it is useful: killing cancer cells, sterilising equipment, tracing leaks in pipes, and dating ancient objects with carbon-14.

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Gravity holds the whole system together

Every mass attracts every other mass. The Sun's gravity holds the planets; a planet's gravity holds its moons. The force gets weaker with distance, which is why outer planets orbit more slowly and take far longer to go round.

Day, year and seasons come from motion

A day is one spin of the Earth on its axis. A year is one trip round the Sun. The seasons come from the Earth's tilt — not from being closer to the Sun. When your hemisphere leans towards the Sun, its light arrives more directly and days are longer, so it is summer.

Stars are born, live and die

A cloud of gas and dust collapses under gravity, heats up, and starts fusing hydrogen — a star is born. It spends most of its life stable, with gravity pulling in and radiation pushing out in balance. When the hydrogen runs out, what happens next depends on mass: small stars swell to red giants and fade to white dwarfs, massive ones explode as supernovae and leave neutron stars or black holes.

Redshift and the expanding universe

Light from distant galaxies is stretched towards the red end of the spectrum, and the further away a galaxy is, the more it is stretched. That means everything is moving apart. Run it backwards and everything was once together — the Big Bang.

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