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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
Ep=-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
Ek=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/NA
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/NA
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
Ek=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