Käsitetakomo concept cards

Physics and the scientific method

Physics

An experimental natural science that studies the basic phenomena and structures of nature and the laws that describe them.

Empirical science

Knowledge is based on observations, measurements and experiments.

Scientific method

A way of building reliable knowledge that combines observations, assumptions, experiments and models.

Hypothesis

A justified assumption that can be tested by experiment.

Physical theory

A broad explanatory framework that links observations and makes it possible to predict new phenomena.

Model

A simplified description of reality used to explain phenomena or make predictions.

Range of validity

The conditions and limits within which a model can be used reliably.

Measurement and errors

Quantity

A measurable property, such as length, mass or time.

Unit

An agreed reference value in which a measured property is expressed.

Measurement result

The value of a quantity, made up of a number and a unit.

Measurement error

The difference between a measured value and the true value of the quantity.

Random error

A varying deviation whose effect can be reduced by repeating the measurement and taking the mean.

Systematic error

A deviation always in the same direction, caused for example by a faulty instrument or method.

Gross error

An obvious deviation caused for example by a misreading, a wrong entry or misuse of an instrument.

Significant figures

The digits of a number that show the precision available in a measurement result.

Resolution of an instrument

How small a change a measuring instrument can reliably detect.

The SI system and orders of magnitude

SI system

The internationally agreed system of units, in which all other units are formed from seven base units.

Base quantity

One of the seven measurable properties chosen as a basis, such as length, mass or time.

Base unit

The unit agreed for a base quantity, such as the metre, the kilogram or the second.

Derived unit

A combination of base units, such as m/s for velocity or N for force.

Multiple of a unit

A practical unit for very large or small values, formed with a prefix.

Prefix

A symbol in front of a unit that gives a power of ten, such as kilo $10^{3}$ or milli $10^{-3}$.

Power of ten

The form $10^{n}$ makes very large and very small numbers easier to write and compare.

Order of magnitude

The size of an object described with a suitable power of ten.

The basic structures of the universe

Elementary particle

One of the smallest known building blocks of matter, such as quarks and leptons.

Quark

A building block of protons and neutrons; ordinary matter contains mainly up and down quarks.

Lepton

A group of elementary particles to which the electron belongs.

Proton

A positively charged particle of the atomic nucleus, made of quarks.

Neutron

An electrically neutral particle of the atomic nucleus, made of quarks.

Atomic nucleus

The dense centre of an atom where the protons and neutrons are.

Atom

A building block of matter made up of a nucleus and the electrons around it.

Molecule

A bound group of two or more atoms.

Planetary system

A star and the planets, small bodies and other matter that orbit it.

Galaxy

A huge system of stars, gas, dust and other matter held together by gravity.

Cluster of galaxies

A large structure of many galaxies held together by gravity.

Space and the evolution of the universe

Big Bang

The model in which time and space evolved from a very hot and dense initial state.

Expansion of the universe

The average distances between galaxies grow with time.

Redshift

The spectral lines of a distant object are shifted to longer wavelengths, which shows that it is receding.

Exoplanet

A planet that orbits another star outside the Solar System.

Red giant

A stage in which a star expands as its hydrogen runs low and heavier nuclei begin to fuse.

White dwarf

The dense, hot core left by a medium-sized star, which slowly cools.

Neutron star

An extremely dense remnant of a collapsed massive star, made mostly of neutrons.

Black hole

An extremely dense concentration of mass whose gravity is so strong that not even light can escape.

Modelling and graphs

Physical model

A simplification based on measurements that describes a natural phenomenon or structure.

Graphical model

The relationship between quantities shown as a graph in a coordinate system.

Mathematical model

The relationship between quantities expressed as an equation.

Quantitative model

A description based on numerical values that allows numerical predictions.

Linear model

A straight line describing a steady change; its slope stays constant.

Line of best fit

A straight line fitted to the measured points that shows the general relationship in the data.

Slope

The change in the quantity on the vertical axis divided by the change in the quantity on the horizontal axis.

Physical slope

The steepness of a graph read as a quantity with its unit and its meaning in the phenomenon.

Interpolation

Using a model to estimate a value between the measured points.

Extrapolation

Extending a model beyond the measured range; the prediction is usually less certain.

Density and motion

Density

The mass of a substance per unit volume.$$\rho = \dfrac{m}{V}$$

Direct proportionality

When one quantity doubles, so does the other, and the graph passes through the origin.

Position

Where an object is in a chosen coordinate system at a given instant.

Uniform motion

The position changes by equal amounts in equal time intervals.

Velocity

The change in position per unit time, together with the direction of motion.

Average velocity

The whole displacement divided by the time it took.

Acceleration

The change in velocity per unit time.$$a = \dfrac{\Delta v}{\Delta t}$$

Free fall

Motion in which air resistance is neglected and only the weight acts on the object.

Acceleration of free fall

Near the Earth the speed changes by about $9.81\,\text{m/s}$ every second.$$g \approx 9.81\,\text{m/s}^2$$

Experimental investigation

Research question

A precise question that an investigation aims to answer.

Experimental plan

A description, written in advance, of the measurements, the equipment and how the investigation is carried out.

Series of measurements

A set of measurement results collected systematically from the same phenomenon.

Repeatability

A well-described experiment can be done again with similar results.

Data

The values, observations, pictures or videos collected in an experiment for analysis.

Analysis of results

Processing the data with calculations and graphs to find relationships.

Conclusion

A justified answer to the research question drawn from the results.

Source of error

A factor that can cause a deviation or uncertainty in a measurement result.

Reliability

An assessment of how well the method and the results support the conclusion.

Report

A written account of the research question, method, results, conclusions and evaluation.

Finding information

Finding information

Searching for reliable information, for example in research, textbooks, databases and expert sources.

Source of information

The background and purpose of whoever publishes information affect how it should be assessed.

Source criticism

Assessing the reliability of a source by its author, reasoning, currency and other sources.

Material

A text, picture, table, graph or other source of information from which conclusions are drawn.

Objectivity

The aim of describing observations independently of the researcher's personal opinions.

Energy in the environment and society

Energy source

A substance or phenomenon used to produce useful energy.

Renewable energy source

A natural resource or phenomenon that is replenished fast enough for human use.

Non-renewable energy source

A natural resource of limited amount that does not form again quickly.

Carbon-neutral energy source

Its use does not increase the concentration of greenhouse gases in the atmosphere in the long term.

Radiant energy

The form of energy that travels from the Sun to the Earth and drives most of the Earth's energy flows.

Infrared radiation

Electromagnetic radiation of longer wavelength than visible light, emitted by the warm ground.

Absorption

Radiation is taken up by matter and the energy it carries passes to the matter.

Reflection

Radiation changes direction at a surface and its energy is not absorbed there.

Climate change

Greenhouse effect

Gases in the atmosphere reduce how much of the Earth's thermal radiation escapes directly to space.

Greenhouse gas

A gas in the atmosphere that absorbs infrared radiation emitted by the Earth.

Carbon dioxide

A greenhouse gas whose concentration grows with the use of fossil fuels.

Methane

A strong greenhouse gas released for example by agriculture and the production of fossil fuels.

Climate change

A long-term change in the Earth's climate; human greenhouse gas emissions intensify the present warming.

Carbon sink

A system that takes up more carbon dioxide from the atmosphere than it releases.

Feedback

A change triggers an effect that can strengthen or weaken the original change.

Emission reduction

Releasing less greenhouse gas into the atmosphere, for example by changing energy production and use.

Energy and forms of energy

Energy

A central quantity of physics that is conserved in every phenomenon but can be transferred and transformed.

Joule

The SI unit of energy.

Form of energy

A way of describing in what form energy appears or is stored.

Kinetic energy

An object has it because it moves; it grows with the mass and the speed.

Potential energy

Stored energy of an interaction; its amount depends on the positions of the objects.

Mechanical energy

Kinetic energy and potential energy together.

Chemical energy

Energy stored in the interactions of atoms and molecules, released for example in burning.

Nuclear energy

Energy of the interactions within atomic nuclei, released in nuclear reactions.

Electrical energy

Energy of electric interactions, easy to transfer in the electricity grid.

Internal energy

Energy of the motion and interactions of the particles of matter.

Conservation of energy

Law of conservation of energy

Energy is neither created nor destroyed; it can be transferred or transformed from one form to another.

Energy transformation

The amount of one form of energy decreases while that of another increases.

Energy transfer

Energy passes from one object or system to another, and the total is conserved.

Energy diagram

A diagram that shows the forms of energy and how they transform and are conserved.

Heat

Energy transferred because of a temperature difference from a hotter object to a colder one.

Wasted energy

Energy that is transformed into a form useless for the device's purpose.

Useful energy

The part of the energy taken in by a device that serves the intended purpose.

Power and energy consumption

Power

How fast energy is transferred or transformed.$$P = \dfrac{\Delta E}{\Delta t}$$

Watt

The SI unit of power, one joule per second.

Input power

How fast a device takes energy from its energy source.

Output power

How fast a device transfers energy to its intended purpose.

Energy consumption

The energy used in a given time can be calculated from the power.$$E = P\Delta t$$

Kilowatt-hour

The energy transferred at a power of one kilowatt in one hour.

Rating plate

A label on a device that shows for example the power it takes from the grid.

Price of electricity

The cost of the electrical energy used is the number of kilowatt-hours times the price per kilowatt-hour.

Efficiency and heating value

Efficiency

The fraction of the energy taken in that is put to use.$$\eta = \dfrac{E_{\text{a}}}{E_{\text{o}}}$$

Efficiency from power

The ratio of output power to input power.$$\eta = \dfrac{P_{\text{a}}}{P_{\text{o}}}$$

Input energy

The total energy a device takes in to operate.

Output energy

The energy a device transfers or transforms for its intended purpose.

Transmission loss

In transmission part of the energy is transformed into an unused form, usually heat.

Heating value

The energy released per unit mass of a fuel when it burns completely.

Energy of combustion

The energy released by a fuel can be calculated from its mass and heating value.$$E = Hm$$

Energy efficiency

The desired benefit is achieved with as little energy and as few losses as possible.

Energy production

Energy production

Turning energy found in nature into a form people can use, such as electricity or heat.

Power plant

A plant where the energy of an energy source is turned into electricity, heat or both.

Generator

A device that turns the energy of rotation into electrical energy.

Turbine

Flowing water, air or steam turns this device, which drives a generator.

Thermal power plant

Thermal energy produces steam, which turns a turbine and a generator.

Condenser

Cools the steam from the turbine back into water and at the same time transfers heat to the surroundings.

Combined heat and power

The same plant produces both electricity and useful heat, which improves the efficiency.

District heating

Centrally produced thermal energy carried by hot water to heat buildings.

Condensing power

Electricity production in which the heat left after the turbine is usually not used for district heating.

Ways of producing energy

Solar power

The Sun's radiant energy is turned directly into electrical energy, for example in a solar panel.

Wind power

The kinetic energy of the air turns a turbine and a generator, which produces electricity.

Hydropower

The potential and kinetic energy of water is turned into electricity with a turbine and a generator.

Bioenergy

Chemical energy bound in organic matter, used for example by burning it.

Fossil fuels

Coal, oil and natural gas are non-renewable fuels whose use increases carbon dioxide emissions.

Nuclear power

Energy released in nuclear reactions boils water, and the steam is used to produce electricity.

Ground-source heat

Thermal energy stored in the soil or bedrock is transferred to heat buildings.

Geothermal energy

Energy from the Earth's internal heat used to produce heat or electricity.

Environmental impacts

Life cycle

The impacts of a way of producing energy are examined from construction and use to dismantling the plant.

Carbon dioxide emission

The climate impact of energy production can be compared by the amount of carbon dioxide released.

Land use

Different ways of production need different areas for plants, fuels and transmission lines.

Natural resources

Energy production uses materials and fuels whose availability and renewal vary.

Impact on ecosystems

Energy production can change habitats, waters and biodiversity.

Health impact

Emissions, accident risks and other factors of production can affect people's health.

Order of magnitude

Ways of production can be compared by the scale of their power, emissions, costs or area.

A flexible energy system

Energy system

The whole made up of the production, transmission, storage and consumption of energy.

Distributed generation

Energy is produced at many small sites close to consumers as well as in large central plants.

Smart grid

A digital grid controls production and consumption and passes information both ways.

Balancing power

Electricity production whose output can be changed quickly to balance production and consumption.

Energy storage

Energy is turned into a form that can be kept and released later when needed.

Thermal storage

Thermal energy is kept for later use, for example in water, soil or the structures of buildings.

Pumped-storage plant

Surplus electricity pumps water uphill, and the energy is stored as potential energy of the water.

Flywheel

Kinetic energy is stored in a rotating body and can later be turned back into electricity.

Microgrid

A local energy grid that links nearby producers, storage and consumers.

A sustainable energy economy

Sustainable energy economy

The ecological, economic and social impacts are considered in the production and use of energy.

Ecological sustainability

Natural resources are used so that the environment's capacity to renew and to carry the load is not put at risk.

Economic sustainability

Energy solutions must be workable in the long run in cost and in the use of resources.

Social sustainability

Energy solutions take into account people's well-being, safety and fair access to energy.

Saving energy

Reducing needless consumption by changing habits and using energy only as needed.

Waste heat

Heat that would otherwise go unused can be recovered and used elsewhere.

Storing energy

Keeping energy for later use evens out the difference in time between production and consumption.

Sustainable consumption

Energy is used efficiently for real needs and its environmental impacts are reduced.

Temperature and the thermodynamic system

Temperature

Describes how vigorous the thermal motion of the particles of matter is.

Kelvin scale

The absolute temperature scale, whose zero $0\,\text{K}$ is the lowest possible temperature.

Absolute zero

The lowest possible temperature, $0\,\text{K}$ or $-273.15\,{}^{\circ}\text{C}$.

Thermal motion

The constant random motion and vibration of the particles of matter.

State variable

A quantity that describes the state of a system, such as temperature, pressure or volume.

Thermodynamic system

The matter or region marked off for study, whose energy changes are examined.

Open system

Both matter and energy can be exchanged with the surroundings.

Closed system

Energy but not matter can be exchanged with the surroundings.

Isolated system

Neither matter nor energy is exchanged with the surroundings.

Thermal equilibrium

The temperatures of systems in contact have become equal.

Thermal expansion and heat transfer

Thermal expansion

Most substances grow when they warm up and shrink when they cool.

Linear thermal expansion

The change in an object's length depends on its original length, the change in temperature and the material.$$\Delta L = \alpha L_0 \Delta T$$

Volume thermal expansion

The change in an object's volume depends on its original volume, the change in temperature and the material.$$\Delta V = \gamma V_0 \Delta T$$

Heat

Energy transferred because of a temperature difference from a hotter system to a colder one.

Conduction

Energy is transferred through the interactions of the particles of matter without any bulk motion of the matter.

Convection

Energy is carried along with a moving liquid or gas.

Thermal radiation

Energy is transferred as electromagnetic radiation and needs no medium.

Thermal conductor

A material in which energy is transferred efficiently by conduction.

Thermal insulator

A material in which energy is transferred slowly by conduction.

Energy balance

The energy of a system stays constant when as much energy enters it as leaves it.

Force and pressure

Force

Describes the strength of the interaction between two objects.

Weight

The strength of the gravitational interaction between the Earth and an object.$$G = mg$$

Pressure

The force perpendicular to a surface per unit area.$$p = \dfrac{F}{A}$$

Pascal

The SI unit of pressure, one newton per square metre.

Air pressure

The pressure due to the weight of the atmosphere and the collisions of gas molecules.

Standard pressure

An agreed reference pressure of about $101\,325\,\text{Pa}$.

Hydrostatic pressure

The pressure due to the weight of the liquid itself grows with depth.$$p_{\text{h}} = \rho g h$$

Total pressure

The pressure in a liquid is the sum of the pressure at the surface and the hydrostatic pressure.$$p = p_0 + \rho g h$$

Pressure difference

Different pressures in two regions can exert a force on an object.

The state of a gas and its changes

Gas pressure

The collisions of the particles with the container walls cause a pressure observed on the large scale.

Amount of substance

Describes the number of particles of a substance; its unit is the mole.

Mole

The amount of substance that contains about $6.02 \cdot 10^{23}$ particles.

Ideal gas

A simplified model of a gas that neglects the volume of the particles and their interactions.

Ideal gas law

Links the pressure, volume, amount of substance and temperature of a gas.$$pV = nRT$$

Isochoric change

The volume stays constant, so the pressure is directly proportional to the absolute temperature.

Isobaric change

The pressure stays constant, so the volume is directly proportional to the absolute temperature.

Isothermal change

The temperature stays constant, so the pressure and the volume are inversely proportional.$$pV = \text{constant}$$

Boyle's law

At constant temperature the pressure of a gas rises as its volume decreases.$$p_1 V_1 = p_2 V_2$$

Combined gas law

The states of a fixed amount of gas can be compared with an equation in which pressure times volume is divided by temperature.$$\dfrac{p_1 V_1}{T_1} = \dfrac{p_2 V_2}{T_2}$$

Warming and cooling

Heat capacity

The energy needed to raise the temperature of an object by one degree.

Specific heat capacity

The energy needed to raise the temperature of one kilogram by one degree.

Quantity of heat

The energy transferred in a change of temperature can be calculated from the mass and the specific heat capacity.$$Q = cm\Delta T$$

Specific heat capacity of water

Its large value means that much energy is needed to change the temperature of water.

Mixing experiment

In an isolated system the energy received by the parts that warm up equals the energy given up by the parts that cool.

Heating power

How fast energy is transferred to the object being heated.$$P = \dfrac{Q}{\Delta t}$$

Cooling

The temperature of a system falls when energy passes from it to the surroundings.

Warming

The temperature of a system rises when its internal energy grows without a change of state.

Changes of state

Solid

The particles are bound in place and vibrate about their equilibrium positions.

Liquid

The particles are close together but can move relative to each other.

Gas

The particles move almost freely and fill the space available.

Melting

A solid turns into a liquid and takes in energy.

Freezing

A liquid turns into a solid and gives up energy to the surroundings.

Vaporisation

A liquid turns into a gas and takes in energy.

Condensation

A gas turns into a liquid and gives up energy to the surroundings.

Sublimation

A solid turns directly into a gas without a liquid stage.

Deposition

A gas turns directly into a solid without a liquid stage.

Specific latent heat of fusion

The energy needed to melt one kilogram at the melting point.$$Q = sm$$

Specific latent heat of vaporisation

The energy needed to vaporise one kilogram at the boiling point.$$Q = rm$$

Phase diagram and humidity

Phase diagram

Shows the state of a substance as a function of temperature and pressure.

Triple point

The temperature and pressure at which solid, liquid and gas can be in equilibrium at the same time.

Critical point

Above this temperature a gas cannot be liquefied by raising the pressure alone.

Boiling

Vaporisation throughout the liquid, when the vapour pressure reaches the pressure of the surroundings.

Evaporation

Vaporisation from the surface of a liquid, which can happen at any temperature.

Saturated vapour

The gas holds the largest possible amount of the substance's vapour at that temperature.

Relative humidity

The amount of water vapour compared with the largest possible amount at that temperature.

Dew point

The temperature to which air must be cooled for water vapour to start condensing.

Boiling point

The temperature depends on the pressure of the surroundings and rises as the pressure rises.

Mechanical work and internal energy

Mechanical work

The energy transferred by a force is the product of the force and the distance moved in its direction.$$W = Fs$$

Internal energy

The energy of a system made up of the kinetic and interaction energies of its particles.

First law of thermodynamics

Internal energy changes through the heat transferred and the work done on the system.$$\Delta U = Q + W$$

Joule's experiment

Mechanical work turning into internal energy is seen as a rise in the temperature of water.

Work done by a gas

An expanding gas does work on the surroundings as its volume grows.

Work at constant pressure

At constant pressure the work done by a gas depends on the pressure and the change in volume.$$W = p\Delta V$$

Adiabatic change

No heat is transferred between the system and the surroundings, so work changes the internal energy.

Isothermal process

The temperature and the internal energy of an ideal gas stay constant during the process.

Conservation of energy

Energy is neither created nor destroyed; it is transferred and transformed into different forms.

Heat engines

Heat engine

Turns part of the energy received from a hot system into mechanical work.

Hot reservoir

The system at higher temperature from which the engine receives energy as heat.

Cold reservoir

The system at lower temperature to which the engine gives up part of the energy it received.

Waste heat

Energy passed to the colder surroundings that cannot be turned into useful work.

Efficiency

The fraction of the energy received that is turned into useful work.

Cycle

A system goes through changes of state and finally returns to its original state.

Refrigerator

Uses work to move energy from a colder space to warmer surroundings.

Heat pump

Uses external work to move energy from cooler surroundings to the space being heated.

Compressor

Compresses the refrigerant, so its pressure and usually its temperature rise.

Climate and heat

Radiative equilibrium

The Earth's temperature stays steady when the power received equals the power radiated to space.

Greenhouse effect

The atmosphere absorbs part of the Earth's thermal radiation and raises the mean surface temperature.

Greenhouse gas

A gas in the atmosphere that absorbs and emits infrared radiation.

Carbon dioxide

A long-lived greenhouse gas whose concentration grows with the use of fossil fuels.

Albedo

The fraction of the radiation arriving at a surface that is reflected back.

Ice–albedo feedback

Less ice means less reflection and more of the Sun's energy absorbed.

Ocean warming

The large specific heat capacity of water lets the oceans store a large amount of energy.

Sea-level rise

Caused mainly by melting land ice and the thermal expansion of sea water.

Melting of sea ice

Floating ice melting does not in itself raise the sea level significantly.

Climate change

The long-term warming of the Earth changes the energy balance, glaciers, oceans and other parts of the climate system.

Quantities of motion

Position

Where an object is in a chosen coordinate system at a given instant.

Distance travelled

The total length of the path an object has travelled.

Displacement

The change in an object's position, with its direction.$$\Delta x = x_2 - x_1$$

Velocity

The rate of change of position, with the direction of motion.

Speed

The magnitude of the velocity, without its direction.

Average velocity

The whole displacement divided by the time it took.$$v_{\text{avg}} = \dfrac{\Delta x}{\Delta t}$$

Instantaneous velocity

The velocity of an object at a given instant.

Uniform motion

The velocity stays constant, so the position changes by equal amounts in equal time intervals.

Graphs of motion

Position–time graph

Shows an object's position as a function of time.

Tangent to a graph

A straight line that touches the curve at the point studied and gives the instantaneous rate of change.

Slope of the tangent

On a position–time graph it gives the object's instantaneous velocity.

Velocity–time graph

Shows an object's velocity as a function of time.

Area under a graph

The signed area between the velocity–time graph and the time axis gives the displacement.

Acceleration–time graph

Shows an object's acceleration as a function of time.

Change in velocity

The signed area under the acceleration–time graph gives the change in velocity.

Graphical differentiation

A new graph of the rate of change is made from the slopes of a graph.

Accelerated motion

Acceleration

The rate of change of velocity.$$a = \dfrac{\Delta v}{\Delta t}$$

Average acceleration

The total change in velocity divided by the time it took.

Instantaneous acceleration

The rate of change of velocity at a given instant.

Constant acceleration

The acceleration stays the same, so the velocity changes steadily.

Velocity in uniformly accelerated motion

The velocity changes steadily with time.$$v = v_0 + at$$

Position in uniformly accelerated motion

The position follows from the initial position, the initial velocity and the acceleration.$$x = x_0 + v_0 t + \tfrac{1}{2}at^2$$

Acceleration of free fall

The magnitude of the acceleration of a freely falling object near the Earth.$$g \approx 9.81\,\text{m/s}^2$$

Free fall

Motion in which only the weight acts on the object and air resistance is neglected.

Interaction and Newton's laws

Interaction

Something between two objects in which they can change each other's motion or shape.

Force

Describes the strength of an interaction; its unit is the newton.

Newton's first law

An object keeps its state of motion if the net force on it is zero; the law of inertia.

Inertia

The property of an object to resist a change in its state of motion.

Newton's second law

A net force gives an object an acceleration; the fundamental law of dynamics.$$\Sigma\overline{F} = m\overline{a}$$

Net force

The vector sum of the forces acting on an object.

Newton's third law

In an interaction the objects exert equal but opposite forces on each other.

Action and reaction

Two equal and opposite forces acting on different objects in the same interaction.

Forces and the equation of motion

Free-body diagram

A drawing that shows every force acting on the object studied as an arrow.

Weight

The gravitational force the Earth exerts on an object.$$G = mg$$

Normal force

The force a surface exerts on an object, perpendicular to the surface.

Tension

The force a taut string or rope exerts on an object, along the string.

Equation of motion

Newton's second law applied: the sum of the forces on an object is linked to its acceleration.

Component of a force

The part of a force in a chosen direction of the coordinate system.

Component form

The equation of motion is written separately, for example in the horizontal and vertical directions.

Condition of equilibrium

In translational equilibrium the vector sum of the forces on an object is zero.$$\Sigma\overline{F} = \overline{0}$$

Inclined plane

The situation becomes easier when the axes are chosen along the plane and the forces are split into components.

Friction, drag and buoyancy

Friction

A force between surfaces in contact that opposes their relative motion or the start of it.

Static friction

Prevents surfaces from sliding over each other and adjusts to the size needed, up to its maximum.

Kinetic friction

Opposes the motion of surfaces sliding over each other (sliding friction).$$F_{\mu} = \mu N$$

Coefficient of friction

A dimensionless number that depends on the pair of materials and describes the friction between the surfaces.

Drag of the medium

A gas or liquid exerts a force on a moving object that opposes its motion.

Air resistance

The drag force of the air on an object usually grows with the speed.

Terminal velocity

The constant velocity reached when the drag and the other forces along the motion cancel.

Buoyancy

The upward force a liquid or gas exerts on an object.

Work and mechanical energy

Mechanical work

A force transfers energy to or from an object during a displacement.$$W = Fs\cos\alpha$$

Kinetic energy

The energy of motion depends on the mass and the speed.$$E_{\text{k}} = \tfrac{1}{2}mv^2$$

Potential energy

The energy of a conservative interaction depends on the positions of the objects.

Gravitational potential energy

The energy related to gravity near the Earth.$$E_{\text{p}} = mgh$$

Conservative force

The work done by the force depends only on the start and end positions, not on the path.

Mechanical energy

The sum of kinetic energy and potential energy.$$E_{\text{mech}} = E_{\text{k}} + E_{\text{p}}$$

Conservation of energy

In an isolated system the total energy stays constant.

Conservation of mechanical energy

Mechanical energy is conserved when only conservative forces do work.

Work–energy principle of mechanics

The change in mechanical energy equals the work done by the non-conservative forces.$$\Delta E_{\text{mech}} = W_{\text{other}}$$

Work–kinetic energy principle

The work done by the net force on an object equals the change in its kinetic energy.$$W_{\text{total}} = \Delta E_{\text{k}}$$

Momentum, impulse and collisions

Momentum

The product of an object's mass and velocity, a vector quantity.$$\overline{p} = m\overline{v}$$

Impulse

Describes the total effect of a force over a time; for a constant force:$$\overline{I} = \overline{F}\Delta t$$

Impulse–momentum principle

The impulse an object receives equals the change in its momentum.$$\overline{I} = \Delta\overline{p}$$

Force–time graph

The area between the graph and the time axis gives the impulse the object receives.

Conservation of momentum

The total momentum of an isolated system does not change in an interaction.

Collision

A short interaction in which the velocities and momenta of the objects can change quickly.

Elastic collision

Besides the total momentum, the total kinetic energy of the objects is also conserved.

Inelastic collision

The total momentum is conserved, but part of the kinetic energy turns into other forms.

Perfectly inelastic collision

After the collision the objects move together at the same velocity.

One-dimensional collision

The objects move along one line, so the directions of momentum can be handled with signs.

Moment and equilibrium

Statics

The part of mechanics that studies the equilibrium of objects at rest.

Equilibrium

A state in which neither the translational nor the rotational motion of an object changes.

Moment

A quantity that describes the turning effect of a force.$$M = Fr$$

Turning effect

The effect of a force that tends to rotate an object.

Axis of rotation

The line about which an object rotates or could rotate.

Line of action

The line through the point of application of a force, in the direction of the force.

Lever arm

The perpendicular, that is shortest, distance between the axis of rotation and the line of action of the force.

Net moment

The sum of the moments of the forces on an object about the chosen axis.

Equilibrium condition for translation

An object does not accelerate when the vector sum of the forces on it is zero.$$\Sigma\overline{F} = \overline{0}$$

Equilibrium condition for rotation

The rotation of an object does not change when the sum of the moments on it is zero.$$\Sigma M = 0$$

Centre of gravity

The point at which the whole weight of an object can be thought to act.

Base of support

The area bounded by the points where an object touches its support; the centre of gravity must be above it for the object not to topple.

Circular motion

Circular motion

Motion along a circular path.

Uniform circular motion

Motion on a circle in which the speed stays constant but the direction keeps changing.

Speed along the path

The speed of an object moving along a circular path.$$v = \dfrac{2\pi r}{T}$$

Centripetal acceleration

The acceleration towards the centre of the circle.$$a_{\text{n}} = \dfrac{v^2}{r}$$

Radius of the path

The distance from the centre of the path to the object moving on it.

Revolution

One full turn on a circular path.

Net force in circular motion

In uniform circular motion the sum of the forces points to the centre and causes the centripetal acceleration.$$\Sigma F = \dfrac{mv^2}{r}$$

Gravitation and planetary motion

Gravitational interaction

The always attractive interaction between objects with mass.

Gravitational force

The force with which two objects with mass attract each other.

Law of universal gravitation

The gravitational force is proportional to the product of the masses and inversely proportional to the square of the distance.$$F = \gamma\dfrac{m_1 m_2}{r^2}$$

Gravitational constant

A constant of nature that sets the strength of the gravitational interaction.$$\gamma \approx 6.67 \cdot 10^{-11}\,\text{N}\cdot\text{m}^2/\text{kg}^2$$

Gravitational field

The region around an object with mass in which another object feels a gravitational force.

Gravitational field strength

The gravitational force on an object per unit mass.$$g = \dfrac{F}{m}$$

Planetary motion

The motion of a celestial body or satellite governed by the gravitational interaction.

Satellite

An object that orbits another object because of gravity.

Orbit

The path a satellite or celestial body follows around its central body.

Orbital period

The time for one full orbit around the central body.

Geostationary orbit

A circular orbit above the equator on which a satellite's period is one day, so it seems to stay still in the sky.

Oscillation

Periodic motion

Motion in which the same state of motion repeats at regular intervals.

Oscillation

Periodic back-and-forth motion about an equilibrium position.

Swinging motion

Periodic motion in which an object moves back and forth along a curved path.

Oscillator

An object or system that oscillates.

Equilibrium position

The position in which the net force on the oscillator is zero.

Displacement

The oscillator's distance from the equilibrium position, with its direction.

Amplitude

The largest displacement of the oscillator from the equilibrium position.

Period

The time for one full oscillation.$$T = \dfrac{1}{f}$$

Frequency

The number of full oscillations per unit time.$$f = \dfrac{1}{T}$$

Damping

The decrease of the amplitude as energy passes to the surroundings, for example through friction or drag.

Simple harmonic motion

Spring force

The restoring force produced by the deformation of a spring.

Hooke's law

The spring force is directly proportional to the extension or compression of the spring.$$F = -kx$$

Spring constant

A quantity that describes the stiffness of a spring; the larger $k$, the stiffer the spring.

Harmonic force

A restoring force directly proportional to the displacement and directed towards the equilibrium position.

Simple harmonic motion

Oscillation in which the displacement varies sinusoidally with time.

Harmonic oscillator

An oscillator whose period does not depend on the amplitude, because the restoring force is directly proportional to the displacement.

Mass–spring oscillator

An oscillating system made of a spring and an object attached to it.$$T = 2\pi\sqrt{\dfrac{m}{k}}$$

Pendulum

A suspended object that swings to both sides of its equilibrium position under its weight.

Simple pendulum

A point-like object swinging on a massless string; for small angles:$$T = 2\pi\sqrt{\dfrac{l}{g}}$$

Natural frequency

The frequency at which a system oscillates freely after a disturbance.

Resonance

A strong growth of the amplitude when the frequency of an external drive matches the system's natural frequency.

Spring potential energy

The energy stored in a stretched or compressed spring.$$E_{\text{p}} = \tfrac{1}{2}kx^2$$

Basics of wave motion

Wave motion

An oscillation travelling from place to place so that energy is transferred but the matter does not travel with it.

Mechanical wave

An oscillation passing through a material medium from particle to particle.

Source of a wave

An oscillator that starts a wave in the surrounding medium.

Medium

A gas, liquid or solid in which a mechanical wave travels through the interactions of its particles.

Pulse

A single disturbance travelling through a medium.

Transverse wave

A wave in which the medium oscillates perpendicular to the direction of travel.

Longitudinal wave

A wave in which the medium oscillates along the direction of travel.

Wavelength

The distance between two neighbouring points in the same phase of oscillation.

Wave speed

The speed at which a disturbance travels through a medium; it depends on the properties of the medium.

Fundamental equation of wave motion

The link between the wave speed, the frequency and the wavelength.$$v = \lambda f$$

Wave phenomena

Reflection

A wave changes direction at a boundary so that it returns into the original medium.

Diffraction

A wave bends and spreads at the edge of an obstacle or a narrow opening.

Interference

The combined effect of two or more waves where they meet.

Constructive interference

Waves that meet in phase have displacements in the same direction, so the amplitude of the resultant wave grows.

Destructive interference

Waves that meet in opposite phase have opposite displacements, so the amplitude of the resultant wave shrinks.

Resultant wave

The wave formed by the combined effect of two or more waves that meet at the same place.

Spectrum

A presentation of which frequencies an oscillation or wave contains and how strong they are.

Beats

A periodic variation in loudness caused by the interference of two waves of nearly equal frequency.

Standing waves

Standing wave

A wave pattern formed by the interference of two identical waves travelling in opposite directions; its nodes stay in place.

Node

A point of a standing wave where the amplitude of oscillation is zero.

Antinode

A point of a standing wave where the amplitude of oscillation is largest.

Fundamental frequency

The lowest possible natural frequency of an oscillating system.

Overtone

A natural frequency of the system higher than the fundamental frequency.

Natural wavelength

A wavelength at which a standing wave that fits the system's boundary conditions can form.

Pipe closed at one end

A pipe with one end closed and one open; a node forms at the closed end and an antinode at the open end.

Pipe open at both ends

A pipe with both ends open, so an antinode of the standing wave forms at each end.

Sound

Sound

A mechanical wave that travels in a gas, a liquid or a solid but not in a vacuum.

Sound wave

A longitudinal wave of compressions and rarefactions travelling through a medium.

Pitch

The perception determined mainly by the frequency of the sound.

Loudness

The perception affected mainly by the sound intensity level and the frequency.

Timbre

The property that tells apart different sound sources playing at the same pitch.

Partial

A single oscillation component of a sound with a given frequency.

Doppler effect

The change in the observed frequency when the source and the observer move relative to each other.

Sound intensity and hearing

Sound intensity

The sound energy passing through unit area per unit time.$$I = \dfrac{P}{A}$$

Sound intensity level

A logarithmic quantity in decibels that compares the intensity of a sound with the threshold of hearing.$$L = 10\,\text{dB} \cdot \lg\dfrac{I}{I_0}$$

Threshold of hearing

The lowest sound intensity a person can hear at a given frequency; at $1\,\text{kHz}$:$$I_0 \approx 10^{-12}\,\text{W/m}^2$$

Range of hearing

The range of frequencies a person can hear; about $16\,\text{Hz}$–$20\,\text{kHz}$.

Noise

Unwanted or disturbing sound.

Infrasound

Sound whose frequency is below the lower limit of human hearing.

Ultrasound

Sound whose frequency is above the upper limit of human hearing.

Magnetism

Magnetic field

A region in which a force acts on a magnetic material or a moving charge.

Magnetic flux density

The quantity $B$ that describes the strength of a magnetic field; its unit is the tesla.

Lorentz force

The force that a magnetic field exerts on a moving charge.$$F = qvB\sin\alpha$$

Force on a current-carrying wire

The force on a wire carrying a current in a magnetic field.$$F = IlB\sin\alpha$$

Magnetic flux

The amount of magnetic field passing through a surface, when the field is perpendicular to the surface.$$\Phi = BA$$

Solenoid

A coil inside which a uniform magnetic field forms when a current flows.

Electromagnetic induction

Faraday's law of induction

A changing magnetic flux induces a voltage.$$e = -N \cdot \dfrac{\Delta\Phi}{\Delta t}$$

Lenz's law

An induced current opposes the change that caused it.

Generator

A device that turns kinetic energy into electrical energy by induction.

Transformer

A device that changes the size of an alternating voltage in the ratio of the numbers of turns in its coils.

Alternating current

A current whose direction and size change periodically.

RMS value

The value of an alternating current that has the same heating effect as an equal direct current.

Light as an electromagnetic wave

Electromagnetic wave

A travelling oscillation of electric and magnetic fields that needs no medium.

Speed of light

The speed of electromagnetic radiation in a vacuum.$$c \approx 3.00 \cdot 10^{8}\,\text{m/s}$$

Refractive index

The ratio of the speed of light in a vacuum to its speed in a material.$$n = \dfrac{c}{v}$$

Snell's law

The law of refraction: the angles of incidence and refraction depend on the refractive indices of the materials.$$n_1\sin\alpha_1 = n_2\sin\alpha_2$$

Total internal reflection

Light is reflected entirely back into the denser material when the critical angle is exceeded.

Diffraction grating

An optical component whose slits diffract light and split it into a spectrum.

Polarisation

Restriction of the direction of the light’s oscillation to one plane.

Focal length of a lens

The distance at which rays parallel to the optical axis are brought to a point.