Physics Laws, Definitions and Equations

Physics Laws, Definitions and Equations

by Andrall Bernard

Heat topics:

​Boyle's Law

Charles' Law

Pressure Law

Heat Capacity

Specific Heat Capacity

​Specific latent heat of Fusion

Specific Latent Heat of Evaporation

​Boyle's Law

The pressure of a given quantity of a gas is directly proportional to the reciprocal of it's volume, provided that temperature and the number of particles remain constant (Decrease Volume, pressure will increase, increase volume, pressure will decrease).

In summary,

1) Pressure is directly proportional to the reciprocal of volume.

p ∝ 1/V

therefore

p= k/V

and so

pV = k

2) The product (pressure x volume) is a constant for all values of pressure .

𝑝₁𝑣₁=𝑝₂𝑣₂

3) Pressure is inversely proportional to volume.​

​Charle's Law

Charle's Law states that the volume occupied by a gas is directly proportional to the absolute temperature, provided that the pressure and number of particles remain constant.

V ∝ T

V = constant x T = kT

V/T = constant

V₁/T₁ = V₂/T₂​

​Pressure Law

The pressure law states that the pressure of a gas is directly proportional to the (absolute) temperature, provided that the volume and number of particles (n) are held constant.

This can be stated as,

P ∝ T

P₁/T₁ = P₂/V₂​

​Heat Capacity

​The heat capacity (C) of an object is defined as the heat required to raise its temperature by one degree. Heat capacity has units J K^-1

​

The equation for heat capacity may be written out as follows,

C=QΔT

Specific Heat Capacity​

The specific heat capacity (c) of a substance is the amount of heat required to raise the temperature of 1kg of the substance by one degree. Specific Heat capacity has units J kg^-1.

​

Equation:

Q=mcΔT​

​Specific Latent Heat of Fusion

​Specific latent heat of fusion, l_f, of a substance is defined as the amount of heat required to change a unit mass of the substance from solid to liquid state, without any change in the temperature.

​Specific Latent Heat of Evaporation

This is the heat required to convert 1 kg of a substance at a fixed temperature from liquid to gaseous (vapour) state.

Note: Measured in J kg^-1

Equation: Q=mL

Where,

Q= Heat change

m= mass

L= specific latent heat​

​Light Topics:

​Snell's Law

Refractive Index

Critical Angle

Focal length of a lens

Principle Focus

Lens Formula

​Snell's Law

Laws of Refraction

1. The incident, the normal and refracted rays all lie in the same plane

2. The sine of the angle of incidence divided by the sine of the angle of refraction is a constant known as the refractive index.

This is known as Snell's Law.

Snell's Law states that

n₁ sin θ₁ = n₂ sin θ₂​

​Refractive Index

Refractive index, also called index of refraction, measure of the bending of a ray of light when passing from one medium into another.

The refractive index is represented by the symbol 1n2 where the 1 refers to the 'incident medium' and the 2 refers to the 'refracting medium'.

i.e.

₁n₂ =

​Critical Angle

​For light travelling to a less dense medium, the angle of incidence for which the angle of refraction is 90 degrees is known as the critical angle.

​note:

N=

​

​where n = refractive index

​and sin c = critical angle

​Focal length of a lens

The focal length of a lens (f) is the distance from the centre of the lens to the principal focus.

this can be represented as,

1/object distance + 1/image distance = 1/ focal length

1/o + 1/i = 1/f​

​Principal Focus

​The principle focus (F) is the point on the principal axis to which initially parallel rays converge , or form which they appear to diverge after refraction at the lens. There are to principal foci (plural of focus), one on each side of the lens.

Lens Formula

​Lens equation or lens formula is an equation that relates the focal length, image distance, and object distance for a spherical mirror. It is given as,

Lens Formula - 1/u + 1/v = 1/f

where.

v = Distance of the image from the lens.

u = Distance of the object from the lens.

f = Focal length of the lens.

​Wave Topics:

Wavelength

Frequency

Amplitude

Pitch

Loudness

Quality

Transverse wave

Longitudinal wave

Wave speed​

​Wavelength

​The wavelength (λ) can be taken as the distance between the midpoints of two adjacent crests or two adjacent troughs. More generally, the wavelength is the distance between one particle and the nearest one which is at the same stage of its motion.( the two particles are said to be in phase they have the same displacement and move in the same direction with the same speed.) Wavelength is measured in metres.

Note: Wavelength is usually denoted by the Greek letter lambda (λ)

The equation for this is,

λ =

​Frequency

​The frequency (f) is equal to the number of oscillations per second or the number of wavelengths that pass a reference point in one second. Frequency is measured in hertz (Hz).

Note: The frequency formula in terms of time is given as: f = 1/T where, f is the frequency in hertz, and T is the time to complete one cycle in seconds. The frequency formula in terms of wavelength and wave speed is given as, f = 𝜈/λ where, 𝜈 is the wave speed, and λ is the wavelength of the wave.

​Amplitude

​The amplitude (A) of a wave is the maximum displacement of any particle on the wave from its rest position or equilibrium position.

Note: Displacement is a vector quantity, measured in metres.

​

​Pitch

​Pitch is a measure of sound that depends on the frequency. Rapidly vibrating objects produce sounds of high frequency (and pitch). Slowly vibrating objects produce sounds of low frequency.

​Loudness

​Loudness of Sound Definition: It refers to how loud or soft a sound seems to a distant listener. The loudness of sound is determined by the intensity or amount of energy present in sound waves and is expressed in decibels. As the level of decibel gets higher sound waves have greater intensity and sounds are louder.

​Quality

​The quality of a sound depends on the manner in which the sounding material vibrates. A musical tone is defined by its pitch, loudness and quality.

​Transverse Wave

​(for) Transverse waves, the direction of movement of the particles or fields is at right angles to the direction of wave travel. Transverse waves include water waves, light and other electromagnetic waves. Transverse waves may be demonstrated using a slinky.

The equation for this is,

v = fλ

​Longitudinal Wave

​In longitudinal waves, particles vibrate about a rest (mean) position in the direction of wave travel. If a slinky is given a pulse, the coils become compressed in some regions and spaced out in others. Longitudinal waves, for example sound waves, travel through the air, through liquids and through solids by a series of compressions and rarefactions. Longitudinal waves are not transmitted in (do not travel through) a vacuum. In a longitudinal wave, the wave energy is transmitted by physical contact between particles or layers of the transmitted medium.

​Wave Speed

It follows from our definitions of period and wavelength that the wave speed is related to wavelength and period.

Speed = Wavelength x Frequency, this equation can be used to calculate wave speed when wavelength and frequency are known.

Electricity​

​Law of electrostatics

Resistors in series

Resistors in parallel

Ohm's Law

Law of magnetism

Right hand grip rule

Fleming's Left hand rule

Fleming's right hand rule

Lenz's Law

Faraday's 2nd law

​Law of electrostatics

​Law of electrostatics states that, Like charges repel each other; unlike charges attract. Thus, two negative charges repel one another, while a positive charge attracts a negative charge. The attraction or repulsion acts along the line between the two charges. The size of the force is proportional to the value of each charge.

​Resistors in series

​Resistors are in series whenever the flow of charge, or the current, must flow through components sequentially. To calculate the total overall resistance of a number of resistors connected in this way you add up the individual resistances. This is done using the following formula: Rtotal = R1 + R2 +R3 and so on.

​Note: If the two resistors of interest have equal voltage drop across them, they are connected in parallel. If the two resistors have equal current flowing trough them, they are connected in series.

​Resistors in Parallel

​Resistors are in parallel if their terminals are connected to the same two nodes. The equivalent overall resistance is smaller than the smallest parallel resistor. When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, so the total resistance is lower. Each resistor in parallel has the same full voltage of the source applied to it, but divide the total current amongst them.

​The following equation can be used,

        =

​Ohm's Law

In the special case where R (resistance) is constant, the relationship:

V = I x R

express Ohm's Law.

Formally, Ohm's law may be stated as follow:

At constant temperature, the potential difference across the ends of a conductor is directly proportional to the current through it.

​

Devices which obey Ohm's law ohmic devices. Those devices which do not obey Ohm's law are called non-ohmic devices.​

​Law of Magnetism

​law of magnetism is that like poles repel one another and unlike poles attract each other; this can easily be seen by attempting to place like poles of two magnets together.

Further magnetic effects also exist. If a bar magnet is cut into two pieces, the pieces become individual magnets with opposite poles. Additionally, hammering, heating or twisting of the magnets can demagnetize them, because such handling breaks down the linear arrangement of the molecules. A final law of magnetism refers to retention; a long bar magnet will retain its magnetism longer than a short bar magnet.

Right hand grip rule​

​The right hand grip rule states that if a conductor carrying a current is gripped with the right hand, with the thumb pointing along the conductor in the direction of conventional current, the curl of the fingers around the conductor indicates the direction of the magnetic lines of force.

​Fleming's Left hand rule

​Fleming's left hand rule states that, if the forefinger, second finger and thump of the left hand are held at right angles to one another, and if the forefinger points in the direction of the field and the second finger in the direction of the current, then the thumb points in the direction of the force which is acting on the conducter carrying the current.

​Fleming's right hand rule

​If the thumb and first two fingers of the right hand are held mutually at right angles, with the first finger in the direction of the magnetic field and the thumb in the direction of motion, then the second finger shows the direction of the induced current.

​Lenz's law

​Lenz’s law, in electromagnetism, statement that an induced electric current flows in a direction such that the current opposes the change that induced it. This law was deduced in 1834 by the Russian physicist Heinrich Friedrich Emil Lenz.

​The equation is as follows:

​

​Where:

ε = Induced emf ( Electromotive force)

δΦ_B = change in magnetic flux

N = No of turns in coil

​Faraday's Second Law

​Faraday's second law of electrolysis states that ''The masses of different ions liberated at the electrodes, when the same amount of electricity is passed through different electrolytes are directly proportional to their chemical equivalents”.

​Mechanics Topics:

Hooke's Law

Newton's First law

Newton's Second law

Newton's Third law

Density

Relative Density

Pressure

Scalar quantity

Vector quantity

Moment

​

​​Law of Moments

​Work

​​Principle of Conservation of Energy

Momentum

​Principle of Conservation of Momentum

​Kinetic Energy

​Gravitational Potential Energy

​Power

​Watt

​​Efficiency

​Average Speed

​Average Velocity

​Acceleration

​Centre of Gravity

​Constant acceleration equations of motion (4 eqns)

Hooke's Law​

​Hooke's law states that extension is directly proportional to load or applied force, provided the elastic limit is not exceeded.

Equation: F = kx

​Newton's First law

​Newton's first law of motion states that, an object at rest tends to stay at rest and an object in motion tends to stay in motion with the same velocity, unless the object is acted upon by an unbalanced force.

​Newton's Second law

​Newton's second law predicts the behaviour of objects for which all existing forces are not balanced.

Note:

* Newton's second law does not imply that motion always results when a force is applied: e.g. the shape may change.

* Acceleration may involve a change of direction or a change of velocity.

* Equal forces which are not acting along the same line cause motion.

* When equal but opposite forces act along the same line, they cancel each other's effect and no motion occurs.

​Newton's Third law

​For every action there is an equal and opposite reaction.

Can be restated as follows:

Forces exist in pairs- 'equal and opposite action-

reaction pairs'.

​Density

​The greater the volume of a given material, the greater the mass:

mass(m) ∝ volume(V)

or

m= p x V

The constant proportionality p is known as the density of the material. Density is defined as the mass per unit volume of a given substance.

Note:

The units of density are kg m^-3 (SI) or g cm^-3.

​Relative Density

​The relative density pr measures how many times a given material is denser than water.

Relative density (pr) = density of material/ density of water

Relative density is a ratio. It is dimensionless quantity, i.e. it has no units.

Relative density may also be defined as:

mass of a given volume of material/mass of the same volume of water.

​Pressure

​An object exerts a pressure on any surface with which it is in contact. Pressure is related to force as follows:

pressure (p) = force (F)/ area (A)

​

Pressure is the force acting perpendicular to unit surface area. The SI unit of pressure is N m-2, also called the pascal (Pa).

​Scalar quantity

​Physical quantities that have size (magnitude) only are called scalar quantities.

​Vector quantity

Quantities such as displacement, velocity, acceleration, force and momentum have both size (magnitude) and direction. They are vector quantities.​

​Moment

​A force or system of forces may cause an object to turn. A moment is the turning effect of a force. Moments act about a point in a clockwise or anticlockwise direction. The point chosen could be any point on the object, but the pivot - also known as the fulcrum - is usually chosen.

The magnitude of a moment can be calculated using the equation:

moment of a force = force × distance

moment = F x d

Note: A moment which tends to rotate an object or system in a clockwise direction is called a clockwise moment.

* A moment which tends to rotate an object or system in an anticlockwise direction is known as an anticlockwise moment.

​Law of moments

​Law of Moments states that when a body is balanced, the total clockwise moment about a point equals the total anticlockwise moment about the same point. Equation. Moment =force F x perpendicular distance from the pivot d.

​Work

​An object which has the ability to do work is said to have energy. Work is done: things happen whenever energy transfers take place.

Energy and work are measured in joules (j), named after James Prescott Houle (1818-1889)

The joule is defined as the energy transformed or the work done when a force of 1 newton displaces an object a distance of 1 metre in the direction of the force.

Mathematically, work (W) is expressed by the equation:

W = F x d cos θ

where F is the force applied, d is the displacement and θ is the angle between the force and the displacement vectors.

Principle of Conservation of Energy​

​Principle of conservation of energy states that, energy is neither created nor destroyed, only converted to another form, i.e. the total energy present at every stage in a chain of energy conversions is the same.

​Momentum

​Momentum is that physical quantity which takes into account both the mass of an object and its velocity.

​Principle of Conservation of Momentum

​Total momentum of a system remains the same before and after a collision.

​Kinetic energy

​Kinetic energy is the energy that an object has because it is moving.

kinetic energy (in joules) = 1/2 x mass x speed(²)

A doubling of speed leads to quadrupling of kinetic energy; a doubling of mass leads to a doubling of kinetic energy.

​Gravitational potential Energy

​Gravitational potential energy, E_p, of an object may be expressed mathematically as follows:

E_p = mass (kg) x acceleration due to gravity ( N kg ^-1) x height (m)

= m x g x h.

Gravitational potential energy, then, is dependent on two variables:

*mass;

*height above reference position.

​Power

​The power of persons or machines measures how quickly they convert energy from one form to another or how quickly they do work.

Power is the work done or energy converted per unit time.

Power can be expressed by the following equation,

​

Power=

​

Note: Power is measure in watts (w)

​Watt

​Watt, unit of power in the International System of Units (SI) equal to one joule of work performed per second, or to ¹/₇₄₆ horsepower. An equivalent is the power dissipated in an electrical conductor carrying one ampere current between points at one volt potential difference. Most electrical devices are rated in watts.

​Efficiency

​Efficiency is a comparison of the energy output to the energy input in a given system. It is defined as the percentage ratio of the output energy to the input energy.

The efficiency of a machine= energy output/energy input

Efficiency may also be expressed as a percentage.

​

Efficiency can also be given in terms of mechanical advantage and velocity ratio.

​Mechanical advantage

​Mechanical advantage is the ratio of the load moved (overcome) to the effort applied.

M.A. = load/effort

Mechanical advantage is dimensionless (i.e. it has no unit). The mechanical advantage in any situation is affected by the amount of friction involved.

​Velocity ratio

​Velocity ratio is the ratio of the distance moved by the effort to the distance moved by the load.

V.R. = displacement of the effort per second/displacement of the load per second

​

= displacement of load/displacement of effort

Velocity ratio, like mechanical advantage, is dimensionless. However, velocity ratio is not affected by friction.

It can be shown that,

​

%efficiency = mechanical advantage/velocity ratio x 100

​Average Speed

​The speed of an object is an indication of how fast it is moving. If the speed of an object varies during its motion, you need to compute its average speed.

​

average speed = total distance travelled/total time taken.

​Average velocity

​Average velocity is defined as the change in position or displacement divided by the time intervals in which the displacement occurs. The average velocity can be positive or negative depending upon the sign of the displacement. The SI unit of average velocity is meters per second (m/s or ms^-1).

​

This can be demonstrated by,

Average velocity= change in total displacement/total time taken for the change

Acceleration

​Acceleration is defined as the 'rate at which an object changes its velocity'

the equation for acceleration is as follows,

​

Acceleration (a) = change of velocity (∆v)/time (t)

​

Note the following: Acceleration is a vector quantity. It's sign depends on whether the object is speeding up or slowing down. If it is positive, the object is speeding up and the acceleration is in the same direction as the velocity. If it is negative, the object is slowing down or decelerating and the acceleration is in the opposite direction to the velocity.

​Centre of gravity

​The centre of gravity or centre of mass of a body is the point through which the total weight of the body is considered to act.

​Constant acceleration equations of motion

1) ​

​2)

​

​3)

​

​4)   

​Physics of the Atom Topics:

Alpha particles

Beta particles

Gamma rays

Atomic number

Mass number

Isotope

Half-Life ​

​Alpha particles

​This is the type of emission was deflected to a small extent in magnetic fields. The direction of the deflection indicated that a -particles were positively charged. In 1909, Rutherford 'proved' that the a-particle was identical with the helium nucleus.

​Beta particles

​A negatively charged particle (an electron) emitted from the nucleus of an atom during radioactive decay. These were deflected in a magnetic field but in the direction opposite to that of a-particles. B-particles were later shown to be fast-moving electrons.

​Gamma particles

This radiation, being uncharged, was not affected by electric or magnetic fields. It was thought that to be wave-like in nature. This was confirmed by Rutherford and Andrade in 1914. ​

​Atomic Number

​The atomic number (Z) of an element is the number of protons in the nucleus of the atoms of that element. For a neutral atom, the atomic number is equal to the number of orbiting electrons.

​Mass number

​Mass number (A) is the number of protons pls the number of neutrons in the nucleus. Mass number is also called the nucleon number. It follows that:

​

neutron number = mass number - atomic number

= A - Z

​Isotope

​Species that has the same number of protons but has different number of neutrons are called isotopes.

​Half-Life

​For a given radioactive element, there is a specific time during which half the original number of radioactive nuclei will decay. This time is the half-life of the radioactive element.