9702 Physics DEFINITIONS AND EQUATIONS

radian

the angle subtended by the arc of a circle which is equal in length to the radius

radian equation

Θ=s/r

angular displacement

the angle through which an object moves during circular motion, measured in radians

linear speed

the distance travelled by an object per unit time

linear speed equation

v=2πr/T

period (ch12 circular motion)

the time taken to complete one whole revolution

angular speed

the angular displacement of an object per unit time

angular speed equation

⍵=∆Θ/∆t

equation linking linear speed and angular speed

v=r⍵

centripetal force

a force directed towards the centre of the circle and is perpendicular to the velocity of the object to keep an object in circular motion

centripetal force equation using linear speed

F=mv²/r

centripetal force equation using angular speed

F=mr⍵²

centripetal acceleration

the acceleration of an object towards the centre of a circle which is perpendicular to the linear velocity of the object and caused by the resultant force in circular motion

centripetal acceleration equation using linear speed

a=v²/r

centripetal acceleration equation using angular speed

a=r⍵²

equation for horizontal component of tension in circular motion in a conical pendulum

TsinΘ=mv²/r

equation for vertical component of tension in circular motion in a conical pendulum

TcosΘ=mg

field of force (ch13 gravitational fields)

a region of space in which a mass experiences a non-contact force

gravitational field strength at a point

the gravitational force per unit mass at that point

gravitational field strength equation

g=F/m

Newton’s law of gravitation

any two point masses attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres

Newton’s law of gravitation equation

F=Gm₁m₂/r²

equation for gravitational field strength at a point mass

g=GM/r²

gravitational potential at a point

the work done per unit mass in bringing a small test mass from infinity to that point

gravitational potential at a point equation

ɸ=-GM/r

gravitational potential energy equation

E_p=-GMm/r

geostationary orbit

orbit in which a satellite orbits the Earth from west to east, above the equator, and has an orbital period of 24 hours

amplitude

the maximum displacement from the equilibrium position

period (ch17 oscillations)

the time taken to complete one cycle

frequency

the number of oscillations per unit time

frequency equation

f=1/T

angular frequency

the rate of change of angular displacement

angular frequency equation using time period

⍵=2π/T

angular frequency equation using frequency

⍵=2πf

angular frequency equation using time period

⍵=2π/T

angular frequency equation using frequency

⍵=2πf

frequency equation

f=1/T

phase difference

the difference in the relative positions of the crests or troughs of two waves of the same frequency

phase angle equation

phase angle=⍵∆T

simple harmonic motion

a type of oscillation in which acceleration is directly proportional to its displacement and acts in the opposite direction to the displacement

simple harmonic motion equation

a=-⍵²x

simple harmonic motion equation for when an oscillation starts at the equilibrium position at t=0

x=x₀sin⍵t

simple harmonic motion equation for when an oscillation starts at the maximum displacement

x=x₀cos⍵t

equation for the maximum speed in simple harmonic motion

v=v₀cos⍵t

equation linking speed v with the oscillator’s displacement x in simple harmonic motion

v=±⍵√(x₀²-x²)

kinetic energy equation for simple harmonic motion

E_k=½m⍵²x₀²

damping

the reduction of energy and amplitude of oscillations due to resistive forces on the oscillating system

under-damping

amplitude decays exponentially with time

critical damping

returns to rest at equilibrium position in the shortest possible time without oscillating

heavy damping

takes a long time to return to equilibrium position without oscillating

natural frequency

the frequency at which a system will oscillate freely

forced oscillation

periodic forces applied in order to sustain oscillations

driving frequency

the frequency of forced oscillations

resonance

occurs in an oscillating system when the driving frequency is similar to the natural frequency of the system and causes the amplitude to increase significantly

thermal equilibrium

a condition when two or more objects in contact have the same temperature so that there is no net transfer of thermal energy

thermal energy

transferred from a region of higher temperature to a region of lower temperature

absolute zero

the temperature at which atoms have zero energy

equation converting between kelvin and celcius

T(K)=Θ(˚C)+273.15

specific heat capacity

the energy required per unit mass of the substance per unit ˚C to raise the temperature by 1K or 1˚C

specific heat capacity equation

∆Q=mc∆Θ

specific latent heat

the energy required per unit mass of a substance to change its state without any change in temperature

specific latent heat equation

Q=ml

specific latent heat of fusion

the energy required per unit mass of a substance to change it from solid to liquid without any change in temperature

specific latent heat of vaporisation

the energy required per mass of a substance to change it from liquid to gas without any change in temperature

boiling

the process by which a liquid changes into its gaseous state at a specific constant temperature, known as a boiling point

evaporation

the process by which molecules on the surface of a liquid with sufficient kinetic energy break from the attractive forces of the liquid and escape as gas particles

melting

the process by which a solid changes into its liquid state at a constant specific temperature, known as a melting point

mole

the amount of substance which contains the same number of particles as there are in 0.012kg of carbon-12

Avogadro’s constant

the number of atoms of carbon-12 in 0.012kg of carbon-12

relationship between the amount of moles in a substance n and the number of particles N

n=N/N_A

molar mass equation

M=m/n

density of a gas equation

⍴=Nm/V

Boyle’s law

the pressure exerted by a fixed mass of gas is inversely proportional to its volume, provided that the temperature of the gas remains constant

Boyle’s law equation

p₁v₁=p₂v₂

Charle’s law

the volume of a fixed mass is directly proportional to its thermodynamic temperature, provided the pressure of gas remains constant

Charles’ law equation

V₁/T₁=V₂/T₂

pressure law

the pressure of a fixed mass of gas is directly proportional to its thermodynamic temperature, provided the volume of gas remains constant

pressure law equation

p₁/T₁=p₂/T₂

ideal gas

a gas which obeys the equation pV=constant x T, for all values of p, V, and T, in which p is the pressure, V is the volume, and T is the thermodynamic temperature of the gas

ideal gas equation using the molar gas constant

pV=nRT

ideal gas equation using the Boltzmann constant

pV=NkT

equation for the Boltzmann constant

k=R/N_A

Brownian motion

the haphazard or random movement of tiny suspended particles in a fluid

kinetic theory of gases assumptions

The molecules are in rapid, random motion. There are no attractive intermolecular forces between the molecules. The volume of the gases is negligible compared to the volume of occupied by the gas. The gas molecule collisions are perfectly elastic so there is no loss of kinetic energy. The duration of the collisions in negligible compared to the time interval between collisions. The molecules behave like hard spheres and obey Newton’s laws of motion.

kinetic theory of gases equation

pV=⅓Nm⟨c²⟩

kinetic theory of gases equation using density

p=⅓⍴⟨c²⟩

average translational kinetic energy

directly proportional to the thermodynamic temperature

average kinetic energy of a molecule equation

E_k=½m⟨c²⟩=(3/2)kT

work done by a gas equation

W=p∆V

internal energy

the sum of the random distribution of kinetic and potential energies of its molecules

first law of thermodynamics

the increase in internal energy of a closed system is the sum of the thermal energy supplied to the system and the work done on the system

first law of thermodynamics equation

∆U=q+W

electric field

a region of space where a charge experiences an electric force

electric field lines

line spacing represents electric field strength. the lines of force start on a positive charge and end on a negative charge, never touching or crossing

electric field strength

the electric force per unit positive charge

electric field strength equation

F=Eq

electric field strength across a uniform electric field equation

E=∆V/∆d

Coulomb’s law

the force between two point charges is directly proportional to the product of the two charges and inversely proportional to the square of their separation

Coulomb’s law equation

F=Q₁Q₂/4πε₀r²

electric field of a point charge equation

E=Q/4πε₀r²