Some Basic Ideas Every Physics Student Should Know

Vectors and Scalars

A scalar is a physical quantity with magnitude only.
A vector is a physical quantity with magnitude and direction.
Vectors may be represented as arrows where the length of the arrow indicates the magnitude and the arrowhead indicates the direction of the vector.
The direction of a vector can be indicated by referring to another vector or a fixed point; using a compass; or bearing.
The resultant vector is the single vector whose effect is the same as the individual vectors acting together.
A vector has a magnitude and direction.
Vectors can be used to represent many physical quantities that have a magnitude and direction, like forces.
Vectors may be represented as arrows where the length of the arrow indicates the magnitude and the arrowhead indicates the direction of the vector.
Vectors in two dimensions can be drawn on the Cartesian plane.
Vectors can be added graphically using the head-to-tail method or the tail-to-tail method.
A closed vector diagram is a set of vectors drawn on the Cartesian using the tail-to-head method and that has a resultant with a magnitude of zero.
Vectors can be added algebraically using Pythagoras’ theorem or using components.
The direction of a vector can be found using simple trigonometric calculations.
The components of a vector are a series of vectors that, when combined, give the original vector as their resultant.
Components are usually created that align with the Cartesian coordinate axes.

One-Dimensional Motion

A reference point is a point from where you take your measurements.
A frame of reference is a reference point with a set of directions.
Your position is where you are located with respect to your reference point.
The displacement of an object is how far it is from the reference point. It is the shortest distance between the object and the reference point. It has magnitude and direction because it is a vector.
The distance of an object is the length of the path travelled from the starting point to the end point. It has magnitude only because it is a scalar.
Speed is the distance covered divided by the time taken.
Average velocity is the displacement divided by the time taken.
Instantaneous speed is the speed at a specific instant in time.
Instantaneous velocity is the velocity at a specific instant in time.
Acceleration is the change in velocity over a time interval.
The gradient of a position – time graph gives the velocity.
The gradient of a velocity – time graph gives the acceleration.
The area under a velocity – time graph gives the displacement.
The area under an acceleration – time graph gives the velocity.
The graphs of motion are summarised in a previous lesson.
The equations of motion are used where constant acceleration takes place.
Projectiles are objects that move through the air. In vertical projectile motion we deal with objects that fall under the influence of gravity and only vertically.
Objects that move up and down (vertical projectiles) on the Earth accelerate with a constant acceleration which is approximately equal to directed downwards towards the centre of the earth.
The time it takes an object to rise to its maximum height, is the same as the time it will take to fall back to its initial height. The magnitude of the velocity will also be the same but the direction will be reversed. This is known as time symmetry and is a consequence of uniform gravitational acceleration.
The equations of motion can be used to solve vertical projectile problems.
Graphs for vertical projectile motion are similar to graphs for motion at constant acceleration.

Newton’s Laws

The normal force, is the force exerted by a surface on an object in contact with it. The normal force is perpendicular to the surface.
Frictional force is the force that opposes the motion of an object in contact with a surface and it acts parallel to the surface the object is in contact with. The magnitude of friction is proportional to the normal force.
For every surface we can determine a constant factor, the coefficient of friction, that allows us to calculate what the frictional force would be if we know the magnitude of the normal force. We know that static friction and kinetic friction have different magnitudes so we have different coefficients for static friction and kinetic friction.
The components of the force due to gravity, parallel-direction and perpendicular-direction to a slope are given by formula outlined in this lesson.
$\begin{aligned} F_{g x} & = F_{g} \sin (θ) \\ F_{g y} & = F_{g} \cos (θ) \end{aligned}$ Newton’s first law: An object continues in a state of rest or uniform motion (motion with a constant velocity) unless it is acted on by an unbalanced (net or resultant) force.
Newton’s second law: If a resultant force acts on a body, it will cause the body to accelerate in the direction of the resultant force. The acceleration of the body will be directly proportional to the resultant force and inversely proportional to the mass of the body.
Newton’s third law: If body A exerts a force on body B, then body B exerts a force of equal magnitude on body A, but in the opposite direction.
Newton’s law of universal gravitation: Every point mass attracts every other point mass by a force directed along the line connecting the two. This force is proportional to the product of the masses and inversely proportional to the square of the distance between them.

Work, Energy and Power

The gravitational potential energy of an object is the energy the object has because of its position in the gravitational field relative to some reference point.
The kinetic energy of an object is the energy the object has due to its motion.
The mechanical energy of an object is the sum of the potential energy and kinetic energy of the object.
The unit for energy is the joule (J).
The Law of Conservation of Energy states that energy cannot be created or destroyed, but can only be changed from one form into another.
The Law of Conservation of Mechanical Energy states that the total mechanical energy of an isolated system (i.e. no friction or air resistance) remains constant.
Kinetic energy: Energy which a body possesses by virtue of being in motion.
Conservation of Energy: Energy is never created nor destroyed, but is only transformed from one form to another.
Conservation of Mechanical Energy: In the absence of non-conservative forces mechanical energy is conserved.
When a force acting on an object has a component along the line of motion, work is done.
Work is the process of transferring energy from object or system to another.
Energy is the ability to do work.
The work-energy theorem states that the work done on an object by the net force is equal to the change in its kinetic energy.
Power is defined as the rate at which work is done or the rate at which energy is transfered to or from a system.

Momentum and Impulse

Newton’s Second Law: The resultant force acting on a body will cause the body to accelerate in the direction of the resultant force The acceleration of the body is directly proportional to the magnitude of the resultant force and inversely proportional to the mass of the object.
Newton’s Third Law: If body A exerts a force on body B then body B will exert an equal but opposite force on body A.
Momentum: The momentum of an object is defined as its mass multiplied by its velocity.
Momentum of a System: The total momentum of a system is the sum of the momenta of each of the objects in the system.
Principle of Conservation of Linear Momentum: `The total linear momentum of an isolated system is constant’ or `In an isolated system the total momentum before a collision (or explosion) is equal to the total momentum after the collision (or explosion)’.
Elastic collision: both total momentum and total kinetic energy are conserved.
Inelastic collision: only total momentum is conserved, total kinetic energy is not conserved.
Impulse: the product of the net force and the time interval for which the force acts.
Law of Momentum: The applied resultant force acting on an object is equal to the rate of change of the object’s momentum and this force is in the direction of the change in momentum.
Impulse-momentum theorem: the impulse is equal to the change in momentum.

Mechanical Waves and Sound

A medium is the substance or material in which a pulse will move.
A pulse is a single disturbance that moves through a medium.
The amplitude of a pulse is the maximum disturbance or distance the medium is displaced from its equilibrium position (rest).
Pulse speed is the distance a pulse travels per unit time.
Constructive interference is when two pulses meet and result in a bigger pulse.
Destructive interference is when two pulses meet and and result in a smaller pulse.
A wave is formed when a continuous number of pulses are transmitted through a medium.
A crest is the highest point a particle in the medium rises to.
A trough is the lowest point a particle in the medium sinks to.
In a transverse wave, the particles move perpendicular to the motion of the wave.
The amplitude is the maximum distance from equilibrium position to a crest (or trough), or the maximum displacement of a particle in a wave from its position of rest.
The wavelength is the distance between any two adjacent points on a wave that are in phase. It is measured in metres.
The period of a wave is the time it takes a wavelength to pass a fixed point. It is measured in seconds.
The frequency of a wave is how many waves pass a point in a second. It is measured in hertz or s^-1.
Frequency: f = ¹/_T
Period: T = ¹/_f
Speed: v = fλ
A longitudinal wave is a wave where the particles in the medium move parallel to the direction in which the wave is travelling.
Most longitudinal waves consist of areas of higher pressure, where the particles in the medium are closest together (compressions) and areas of lower pressure, where the particles in the medium are furthest apart (rarefactions).
The wavelength of a longitudinal wave is the distance between two consecutive compressions, or two consecutive rarefactions.
The relationship between the period (T) and frequency (f) is given by T = ¹/_f $T = \frac{1}{f}$ or f = ¹/_T. $f = \frac{1}{T}$
The relationship between wave speed (v), frequency (f) and wavelength (λ) is given by v = fλ.
Sound waves are longitudinal waves
The frequency of a sound is an indication of how high or low the pitch of the sound is.
The human ear can hear frequencies from 20 to 20,000 Hz. Infrasound waves have frequencies lower than 20Hz. Ultrasound waves have frequencies higher than 20,000 Hz.
The amplitude of a sound determines its loudness or volume.
The tone is a measure of the quality of a sound wave.
The speed of sound in air is around 340 ms^-1. It is dependent on the temperature, height above sea level and the phase of the medium through which it is travelling.
Sound travels faster when the medium is hot.
Sound travels faster in a solid than a liquid and faster in a liquid than in a gas.
Sound travels faster at sea level where the air pressure is higher.
The intensity of a sound is the energy transmitted over a certain area. Intensity is a measure of frequency.
Ultrasound can be used to form pictures of things we cannot see, like unborn babies or tumours.
Echolocation is used by animals such as dolphins and bats to “see” their surroundings by using ultrasound.
Ships use sonar to determine how deep the ocean is or to locate shoals of fish.
The Doppler effect is a change in observed frequency due to the relative motion of a source and an observer.
The Doppler effect can be observed in all types of waves, including ultrasound, light and radiowaves.
Sonography makes use of ultrasound and the Doppler effect to determine the direction of blood flow.

Electric Charges and Fields

There are two kinds of charge: positive and negative.
Positive charge is carried by protons in the nucleus.
Negative charge is carried by electrons.
Objects can be positively charged, negatively charged or neutral.
Objects that are neutral have equal numbers of positive and negative charge.
Unlike charges are attracted to each other and like charges are repelled from each other.
Charge is neither created nor destroyed, it can only be transferred.
Charge is measured in coulombs (C).
Charge is quantised in units of the charge of an electron -1.6 × 10^-19 C, Q = nq_e.
Conductors allow charge to move through them easily.
Insulators do not allow charge to move through them easily.
Identical, conducting spheres in contact share their charge.
Objects can be positively, negatively charged or neutral.
Coulomb’s law describes the electrostatic force between two point charges and can be stated as: the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
$F = \frac{k Q_{1} Q_{2}}{r^{2}}$ An electric field is a region of space in which an electric charge will experience a force. The direction of the field at a point in space is the direction in which a positive test charge would moved if placed at that point.
We can represent the electric field using field lines. By convention electric field lines point away from positive charges (like charges repel) and towards negative charges (unlike charges attract).
The magnitude of the electric field, E, at a point can be quantified as the force per unit charge We can write this as: E = ^F/_Q where F is the Coulomb force exerted by a charge on a test charge q. The units of the electric field are newtons per coulomb: NC^-1.
The electric field due to a point charge Q is defined as the force per unit charge.
$E = \frac{F}{q} = \frac{k Q}{r^{2}}$ The electrostatic force is attractive for unlike charges and repulsive for like charges.

Electric Circuits

The potential difference across the terminals of a battery when it is not in a complete circuit is the electromotive force (emf) measured in volts (V).
The potential difference across the terminals of a battery when it is in a complete circuit is the terminal potential difference measured in volts (V).
Voltage is a measure of required/done to move a certain amount of charge and is equivalent to JC^-1.
Current is the rate at which charge moves/flows and is measured in amperes (A) which is equivalent to Cs^-1.
Conventional current flows from the positive terminal of a battery, through a circuit, to the negative terminal.
Ammeters measure current and must be connected in series.
Voltmeters measure potential difference (voltage) and must be connected in parallel.
Resistance is a measure of how much work must be done for charge to flow through a circuit element and is measured in ohms (Ω) and is equivalent to VA^-1.
Resistance of circuit elements is related to the material from which they are made as well as the physical characteristics of length and cross-sectional area.
Current is constant through resistors in series and they are called voltage dividers as the sum of the voltages is equal to the voltage across the entire set of resistors.
The total resistance of resistors in series is the sum of the individual resistances.
Voltage is constant across resistors in parallel and they are called current divides because the sum of the current through each is the same as the total current through the circuit configuration.
The total resistance of resistors in parallel is calculated by using the formula in this lesson.
Ohm’s Law states that the amount of current through a conductor, at constant temperature, is proportional to the voltage across the resistor.
Conductors that obey Ohm’s Law are called ohmic conductors; those that do not are called non-ohmic conductors.
We use Ohm’s Law to calculate the resistance of a resistor. R = ^V/ _I.
The equivalent resistance of resistors in series (R_s) can be calculated by using the formula in this lesson.
The equivalent resistance of resistors in parallel (R_p) can be calculated by using the formula in this lesson.
Electrical power is the rate at which electrical energy is converted in an electric circuit.
The electrical power dissipated in a circuit element or device is P = VI and can also be written as P = I²R or P = V²/_R and is measured in joules (J).
The electrical energy dissipated is E = Pt and is measured in joules (J).
One kilowatt hour refers to the use of one kilowatt of power for one hour.
Ohm’s Law governs the relationship between current and potential difference for a circuit element at constant temperature.
Conductors that obey Ohm’s Law are called ohmic conductors; those that do not are called non-ohmic conductors.
Ohm’s Law can be applied to a single circuit element or the circuit as a whole (if the components are ohmic).
Real batteries have an internal resistance.
The external resistance in the circuit is referred to as the load.

Magnetism and Faraday’s Law

Magnets have two poles – North and South.
Some substances can be easily magnetised.
Like poles repel each other and unlike poles attract each other.
The Earth also has a magnetic field.
A compass can be used to find the magnetic north pole and help us find our direction.
The Earth’s magnetic field protects us from being bombarded by high energy charged particles which are emitted by the Sun.
The Aurorae are an effect of the Earth’s magnetic field.
Electromagnetism is the study of the properties and relationship between electric currents and magnetism.
A current-carrying conductor will produce a magnetic field around the conductor.
The direction of the magnetic field is found by using the Right Hand Rule.
Electromagnets are temporary magnets formed by current-carrying conductors.
The magnetic flux through a surface is the product of the component of the magnetic field normal to the surface and the surface area, Φ = BAcos(θ).
Electromagnetic induction occurs when a changing magnetic field induces a voltage in a current-carrying conductor.
The magnitude of the induced emf is given by Faraday’s law of electromagnetic induction.
Electrical generators convert mechanical energy into electrical energy.
Electric motors convert electrical energy into mechanical energy.
There are two types of generators – AC and DC. An AC generator is also called an alternator.
There are two types of motors – AC and DC.
Alternating current (AC) has many advantages over direct current (DC) listed previously.
The root mean square (rms) value of a quantity is the maximum value the quantity can have divided by √2.
RMS values are used for voltage and current when dealing with alternating current.
The average power dissipated in a purely resistive circuit with alternating current is P_av= I_rmsV_rms.

Introducing Electromagnetic Waves

Electromagnetic radiation has both a wave and a particle nature.
Electromagnetic waves travel at a speed of approximately 3 × 10⁸ms^-1 in a vacuum.
The Electromagnetic spectrum consists of the following types of radiation: radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma-rays.
Gamma-rays have the most energy and are the most penetrating, while radio waves have the lowest energy and are the least penetrating.
A wavefront is an imaginary line that connects waves that are in phase.
Huygen’s Principle states that every point of a wave front serves as a point source of spherical, secondary waves. After a time t, the new position of the wave front will be that of a surface tangent to the secondary waves.
Diffraction is the ability of a wave to spread out in wavefronts as the wave passes through a small aperture or around a sharp edge.
When a wave passes through a slit, diffraction of the wave occurs. Diffraction of the wave is when the wavefront spreads out or “bends” around corners.
The degree of diffraction depends on the width of the slit and the wavelength of the wave
The Doppler effect is a change in observed frequency due to the relative motion of a source and an observer.
The Doppler effect can be observed in all types of waves, including ultrasound, light and radiowaves.
Sonography makes use of ultrasound and the Doppler effect to determine the direction of blood flow.
Light is emitted by stars. Due to the Doppler effect, the frequency of this light decreases and the stars appear redder than if they were stationary. This is called a red shift and means that the stars are moving away from the Earth. This is one of the reasons we can conclude that the Universe is expanding.

Optics and Optical Phenomena

Light rays are lines which are perpendicular to the light’s wavefronts. In geometrical optics we represent light rays with arrows with straight lines.
Light rays reflect off surfaces. The incident ray shines in on the surface and the reflected ray is the one that bounces off the surface. The normal is the line perpendicular to the surface where the light strikes the surface.
The angle of incidence is the angle between the incident ray and the surface, and the incident ray, reflected ray, and the normal, all lie in the same plane.
The Law of Reflection states the angle of incidence (θ_i) is equal to the angle of reflection (θ_r) and that the reflected ray lies in the plane of incidence.
Light can be absorbed and transmitted.
The speed of light, c, is constant in a given medium and has a maximum speed in vacuum of 3 × 10⁸ms^-1.
Refraction occurs at the boundary of two media when light travels from one medium into the other and its speed changes but its frequency remains the same. If the light ray hits the boundary at an angle which is not perpendicular to or parallel to the surface, then it will change direction and appear to `bend’.
The refractive index (symbol n) of a material is the ratio of the speed of light in a vacuum to its speed in the material and gives an indication of how difficult it is for light to get through the material.
Optical density is a measure of the refracting power of a medium.
The normal to a surface is the line which is perpendicular to the plane of the surface.
The angle of incidence is the angle defined between the normal to a surface and the incoming (incident) light ray.
The angle of refraction is the angle defined between the normal to a surface and the refracted light ray.
Snell’s Law gives the relationship between the refractive indices, angles of incidence and reflection of two media.
Light travelling from one medium to another of lighter optical density will be refracted towards the normal.Light travelling from one medium to another of lower optical density will be refracted away from the normal.
The critical angle of a medium is the angle of incidence when the angle of refraction is 90° and the refracted ray runs along the interface between the two media.
Total internal reflection takes place when light travels from one medium to another of lower optical density. If the angle of incidence is greater than the critical angle for the medium, the light will be reflected back into the medium. No refraction takes place.
Total internal reflection is used in optical fibres in telecommunication and in medicine in endoscopes. Optical fibres transmit information much more quickly and accurately than traditional methods.
The photoelectric effect is the process whereby an electron is emitted by a substance when light shines on it.
A substance has a work function which is the minimum energy needed to emit an electron from the metal. The frequency of light whose photons correspond exactly to the work function is known as the cut-off frequency.
The number of electrons ejected increases with the intensity of the incident light.
The photoelectric effect illustrates the particle nature of light and establishes the quantum theory.
Emission spectra are formed when certain frquencies of light are emitted by a gas, as a result of electrons in the atmoms dropping from higher to lower energy levels. The pattern of the spectra is charactersistic of the specific gas.
Absorption spectra are formed when certain frequencies of light are absorbed by a material. These photons are absorbed when their energy is exactly the correct amount to raise an electron from one energy level to another.

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Some Foundational Ideas Every Physics Student Should Know | By Topics