Scalars, Vectors and Newton's Laws

Ever wondered why objects move or stay still? It all comes down to forces and Newton's laws.

Scalars have only magnitude (size) and no direction. Examples include speed, distance, time, mass and energy. Vectors have both magnitude and direction and can be negative. Examples include velocity, displacement, acceleration and force.

Velocity is speed in a certain direction, making it a vector quantity. To calculate speed: Speed $m/s$ = distance (m) ÷ time (s).

Remember: Newton's first law states that an object maintains constant velocity unless acted upon by a resultant force. No resultant force means no acceleration!

Newton's second law tells us that Force (N) = mass (kg) × acceleration $m/s²$, or F = ma. This helps us calculate how objects accelerate when forces act on them. Meanwhile, Newton's third law states that every action force has an equal and opposite reaction force $like a book on a table - the table pushes up with equal force$.

Momentum (mass × velocity) is always conserved in collisions when there are no external forces. This conservation principle is crucial for understanding everything from car crashes to billiard ball collisions.

Motion and Stopping Distances

When a vehicle needs to stop, physics explains exactly why it can't do so instantly.

The stopping distance consists of two parts: thinking distance (how far you travel during reaction time) and braking distance (how far you travel while braking). Together, these determine how much space you need to stop safely.

Several factors affect stopping distances. Thinking distance increases with higher speed, poor concentration, tiredness, distractions, or drugs/alcohol. Braking distance increases with higher speed, poor road conditions, bald tyres, worn brake pads, or greater vehicle mass.

Road safety fact: At 70mph, the typical stopping distance is 96 metres – about the length of a football pitch!

The relationship between speed and braking distance is not linear. Doubling your speed quadruples your braking distance because braking distance is proportional to the square of initial velocity. This is because work done to stop = initial kinetic energy = ½mv².

Large decelerations during crashes are particularly dangerous. When a vehicle stops suddenly from high speed, there's a large change in momentum over a very short time, creating enormous forces that can cause serious injuries. That's why safety features like crumple zones and airbags are designed to extend the stopping time.

Energy Stores and Transfers

Energy makes everything happen, but it never disappears - it just changes form.

Energy comes in different forms (or "stores") like kinetic energy (movement), gravitational potential energy (height), and thermal energy (heat). The formulas to calculate these are:

• Change in GPE (J) = mass (kg) × gravitational field strength $N/kg$ × change in height (m)
• Kinetic energy (J) = ½ × mass (kg) × (speed)² $m/s$²

Energy transfer diagrams show how energy flows from one form to another, including any wasted energy. For example, in an electric bulb, electrical energy transfers to light (useful) and heat (usually wasted).

Fascinating fact: The Law of Conservation of Energy states that energy can never be created or destroyed, only transferred from one form to another.

Common energy transfers include:

• Object projected upwards: KE transfers to GPE, then back to KE if it falls
• Moving car braking: KE transfers to thermal energy through friction
• Electric kettle: Electrical energy transfers to thermal energy

Efficiency measures how much useful energy we get compared to the total energy input. To improve efficiency, we can reduce waste output through lubrication or thermal insulation, or recycle waste energy (like using waste heat as an input elsewhere).

Energy sources come in renewable types (solar, wind, tidal, hydroelectric) and non-renewable types (nuclear, fossil fuels). Renewable sources are becoming more important as non-renewable sources are finite and running out.

Waves

Waves are all around us, transferring energy and information without moving matter.

There are two main types of waves. Transverse waves have vibrations perpendicular to the direction of travel $like water waves, EM waves, and seismic S-waves$. Longitudinal waves have vibrations parallel to the direction of travel $like sound waves and seismic P-waves$.

Key wave characteristics include:

• Amplitude: maximum displacement from rest position
• Wavelength: distance between identical points on adjacent waves
• Frequency: number of waves passing a point per second (Hz)
• Period: time for one complete wave

The wave equation links these properties: Wave speed $m/s$ = frequency (Hz) × wavelength (m).

Did you know? To measure the speed of waves, scientists use techniques like recording time differences between two microphones for sound waves, or using a stroboscope for water waves.

When waves move from one medium to another, several things can happen:

• Refraction occurs when waves change direction at a boundary. When entering a denser medium, waves bend towards the normal, slow down, and their wavelength decreases.
• Reflection happens when waves bounce off a surface, with the angle of incidence equaling the angle of reflection.
• Transmission occurs when waves pass through a transparent material.
• Absorption happens when a material takes in the wave energy, often converting it to heat.

Sound and Ultrasound

Sound waves help us communicate and explore the world in fascinating ways.

The human ear is a remarkable detector of sound waves. Sound enters the ear canal and makes the eardrum vibrate. These vibrations pass through tiny bones that amplify them, then into the fluid-filled cochlea where tiny hairs detect different frequencies and create electrical signals that travel to the brain. Most people can hear frequencies between 20Hz and 20,000Hz.

Cool fact: Different parts of the cochlea detect different frequencies - high frequencies at the base and low frequencies at the apex.

Ultrasound refers to sound waves with frequencies above 20,000Hz, which humans can't hear. It has many practical applications:

• In sonar, ultrasound pulses are sent through water, and the time taken for reflections helps calculate distances to objects like the seabed or schools of fish
• In medical scans, ultrasound creates images of internal body structures (like a developing foetus) without harmful radiation
• In industrial settings, it can detect flaws in materials

Infrasound refers to sound waves with frequencies below 20Hz. Seismic P-waves (longitudinal) and S-waves (transverse) are examples of infrasound. P-waves can pass through both solids and liquids, while S-waves only pass through solids. By studying which waves reach different parts of Earth during earthquakes, scientists have determined that Earth's outer core is likely liquid, as it creates an S-wave "shadow zone."

Light and Lenses

Light behaves in predictable ways that help us see and create amazing optical devices.

When light hits a boundary, it can be reflected or refracted. In reflection, the angle of incidence equals the angle of reflection. Smooth surfaces create specular (clear) reflections, while rough surfaces create diffuse reflections.

Refraction occurs when light changes direction as it passes from one medium to another. When entering a denser medium (like air to glass), light bends towards the normal line. Total internal reflection happens when light tries to exit a denser medium at an angle greater than the critical angle - it's completely reflected back inside.

Fascinating fact: Fiber optic cables use total internal reflection to send information via light pulses that bounce along the inside of the cable without escaping.

Lenses focus or spread light depending on their shape. Concave lenses (thinner in the middle) diverge light and produce virtual, upright, reduced images. They're used to correct short-sightedness. Convex lenses (thicker in the middle) converge light and can produce different types of images depending on the object's position. They're used in magnifying glasses and to correct long-sightedness.

Colour is just different wavelengths of light. When white light hits an opaque object, some wavelengths are absorbed and others reflected - we see the reflected colours. Colour filters work by transmitting only certain wavelengths and absorbing others.

Electromagnetic Waves

The electromagnetic spectrum encompasses a huge range of waves with different properties and applications.

All electromagnetic (EM) waves are transverse waves that travel at the same speed in a vacuum $3×10⁸ m/s$. They transfer energy from a source to an observer but differ in wavelength and frequency. The EM spectrum, from longest to shortest wavelength, includes: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

Each type has specific sources and uses:

• Gamma rays (from neutron stars and explosions): kill cancer cells in radiotherapy, sterilise food and equipment
• X-rays $from stars, X-ray machines$: detect cancer, medical imaging
• Ultraviolet (from the sun, UV lamps): disinfect water, security marking
• Visible light (from the sun, stars, bulbs): photography, seeing the world
• Infrared (from heaters, hot objects): thermal imaging, cooking, remote controls
• Microwaves (from microwave ovens, mobile phones): cooking, communications
• Radio waves (from electrical circuits): broadcasting, communications

Health alert: Many EM waves pose health hazards! Gamma and X-rays can mutate DNA and cause cancer, UV can cause sunburn and skin cancer, and microwaves can heat body tissues.

Radio communication works because oscillations (variations in current and voltage) in a transmitting aerial create radio waves that cause similar oscillations in a receiving aerial. Some radio waves are reflected by the ionosphere (a region of charged particles in the atmosphere), allowing them to travel beyond the horizon.

Electromagnetic Waves and Radiation

Electromagnetic waves connect us to the world while radioactive emissions reveal the secrets of atoms.

Different EM waves have different uses and hazards:

• Radio waves: communications, broadcasting
• Microwaves: cooking, satellite communications
• Infrared: heating, thermal imaging
• Visible light: photography, illumination
• Ultraviolet: disinfection, security marking
• X-rays: medical imaging, scanning
• Gamma rays: cancer treatment, sterilisation

The atom has evolved in scientific understanding over time. Today we know it consists of a positively charged nucleus (containing protons and neutrons) surrounded by negatively charged electrons. The nucleus is incredibly small (about 10⁻¹⁴m) compared to the atom (about 10⁻¹⁰m), with most of the mass concentrated in the nucleus.

Historical insight: Rutherford's alpha scattering experiment revolutionised our understanding of atomic structure. When alpha particles were fired at gold foil, most passed straight through but some bounced back - proving atoms were mostly empty space with a dense nucleus.

Electrons exist in orbits or energy levels around the nucleus. When electrons absorb energy, they move to a higher orbit (away from the nucleus). When they emit energy (often as visible light), they move to a lower orbit. Each element has a unique emission/absorption spectrum based on these electron transitions.

Ionisation occurs when enough energy is provided for electrons to completely escape from the atom, creating ions (charged particles). This is a key process in radiation detection and has implications for safety with radioactive materials.

Radioactivity

Radioactive materials emit particles that can be both dangerous and incredibly useful.

There are three main types of radiation:

• Alpha particles (²₄He): helium nuclei with 2 protons and 2 neutrons. They're positively charged, have short range $3-5cm in air$, can't pass through skin, and are stopped by paper. They cause high ionisation.
• Beta particles (β⁻): fast-moving electrons. They have negative charge, medium range, can pass through skin, and are stopped by aluminium. They cause moderate ionisation.
• Gamma rays (γ): high-energy EM waves with no charge or mass. They have long range, pass through skin, and are only slowed by lead or concrete. They cause the least ionisation.

Safety first: Background radiation is all around us from sources like radon gas (50%), medical procedures (13%), food (11%), buildings, and cosmic rays. It's measured using Geiger-Müller tubes or photographic film.

Radioactive decay happens when unstable isotopes release particles to become more stable. In alpha decay, an atom loses 2 protons and 2 neutrons, decreasing its mass number by 4 and atomic number by 2. In beta decay (β⁻), a neutron changes into a proton and an electron, increasing the atomic number by 1 while the mass number stays the same.

The half-life is the time taken for half the unstable nuclei in a sample to decay. It's a measure of how quickly radioactivity decreases, and each isotope has a specific half-life ranging from fractions of a second to billions of years.

Radiation has many practical applications including smoke alarms (alpha), food irradiation (gamma), medical tracers (gamma), thickness gauging (beta), and pipe leak detection (gamma).

Radiation Applications and Nuclear Power

Radiation offers powerful tools for medicine and energy, but requires careful handling.

In medicine, radiation is used in several ways:

• Internal radiotherapy: radioactive seeds (alpha) or implants (beta) are placed near tumours to kill cancer cells
• External radiotherapy: gamma rays, X-rays or protons are directed at tumours from outside the body
• PET scanners: tracers emit positrons (β⁺) that produce gamma rays when they meet electrons, creating detailed images

Energy debate: Nuclear energy has prevented 1.8 million deaths by reducing air pollution from fossil fuels and has prevented 64 gigatons of CO₂ emissions. However, nuclear accidents can contaminate large areas, and waste disposal remains challenging.

Nuclear fission occurs when large nuclei $like uranium-235$ split into smaller nuclei, releasing energy. This powers nuclear reactors, which contain:

• Fuel rods containing uranium-235
• Control rods that absorb neutrons to control the reaction
• Moderators that slow down neutrons
• Coolant that carries heat from the core to generate steam
• Shielding that prevents radiation leaks

Nuclear fusion combines small nuclei to form larger ones, releasing energy. It powers the sun but requires extremely high temperatures and pressures to overcome the repulsion between positively charged nuclei. Fusion has advantages over fission (no radioactive waste, unlimited fuel) but hasn't yet been achieved on a practical scale due to the technical challenges.

When handling radioactive materials, proper precautions are essential. These include wearing protective gear, storing materials safely, monitoring exposure with badges, limiting dose to patients, and having clear emergency procedures for containment.