Mid year Exam formulas and definitions Flashcards
Radian definition
the angle subtended at the centre of a circle by an arc of equal length to the radius of the circle
Angular displacement definition
the angle of arc through which the object has moved from its starting position
Angular speed definition
the angular displacement per unit time
Angular speed equation
angular speed =
angular displacement / time take
ω = ∆θ / ∆t
Angular speed equation for a single revolution
ω = 2π / T
Key equation for speed involving angular speed
speed = angular speed x radius
v = ωr
Newton’s first law (of motion) definition
an object remains at rest or travels at constant velocity unless it is acted on by a resultant force
Centripetal force definition
the resultant force on an object towards the centre of the circle when the object is rotating around that circle at constant speed
Centripetal acceleration definition
the acceleration of an object towards the centre of the circle when the object is rotating at constant speed round that circle
Centripetal acceleration key formulae
a = v² / r
a = rω²
Newton’s second law (of motion) definition
the resultant force on a body is proportional to the rate of change of momentum of the body
Additional circular motion formulas
v = 2πr/T
Fc = mv² / r
F𝒸 = mω²r
Fc = Ft + (-Fg)
∆θ = ω∆t = 2π∆t/T
Resonance
occurs when the frequency of the driving force is equal to the natural frequency of the oscillating system.
The system absorbs the maximum energy from the driver and has maximum amplitude
Simple Harmonic Motion
When acceleration is directly proportional to the displacement and acceleration and displacement are in opposite directions
Additional SHM formulas
Fr = Fs (restoring force and spring force)
a = -ω²x
Xₜ = Xₒsinωt (given start time [ t = 0 ] else is cos)
Vₜ = Vₒcosωt (given start time [ t = 0 ] else is sin)
aₜ = aₒsinωt (given start time [ t = 0] else is cos)
Vₜ = ± ω √Xₒ² - Xₜ²
v = ωₒxₒ
vmax = 2πfA (A is amplitude)
amax = –(2πf)²A
Formulas for SHM MSO (4)
ω² = k/m
a = -k/m . x
T = 2π √m/k
ma = -2kx
Formulas for SHM pendulum (4)
ω² = g/l
a = -x . g/l
T 2π √l/g
sinθ = x/l
Energy in SHM formulas (3)
Eₜₒₜₐₗ = Eₖ + Eₚ
∆W = ∆Eₖ = ∆Eₚ
Eₜₒₜₐₗ = Eₖ₍ₜ₎+ Eₚ₍ₜ₎
Damping
Reduction in amplitude due to resistive forces
Total energy of a system undergoing simple harmonic motion
E₀ = 1/2mω²x₀² = 1/2mv₀²
Internal energy
the sum of the random distribution of kinetic and potential energies of the atoms or molecules in a system
First law of thermodynamics
∆U = q + W
The increase in internal energy of a body is equal to the thermal energy transferred to it by heating plus the mechanical work done on it
If the volume of a gas is constant it can not do any work
Any change at constant temp Q = W as U must equal 0
Any change where no heat is lost or gained Q = 0 and subsequently ∆U = -W
Work done when the volume of a gas changes at constant pressure
W = p∆V
Thermal equilibrium
a condition when 2 or more objects in contact have the same temperature so that there is no net flow of energy between them
To convert temperatures between degrees Celsius and Kelvin
θ (in ºC) = T (in K) – 273.15
T (in K) = θ (in ºC) + 273.15
T ALWAYS in kelvin when dealing with gasses and gas laws
Specific heat capacity
the energy required by unit mass per unit temperature change
Q = mc∆T
P = VI
E = VIt
Specific latent heat of fusion/vaporization
the amount of heat energy per unit mass needed to convert unit mass of solid/liquid to liquid/gas without change in temperature
Q = mL
P = ∆m/∆t . Lv
Energy needed to raise temp and melt or raise temp and vapourise is
Q = mc∆T + ml
Change in energy for 2 different substances is:
Substance that doesn’t change state
Q = m1c1∆ (Toriginal1 - Tfinal)
Substance that changes state
Q = m2c2∆(Tfinal - (Toriginal2)) + m2L2
equate the 2 as they both equal to Q and solve
Boyle’s Law
p₁V₁ = p₂V₂
Charles’s Law
V₁/T₁ = V₂/T₂
Combined equation for fixed mass of gas
p₁V₁/T₁(n₁) = p₂V₂/T₂(n₂)
remove whatever from the equation that is constant to solve for missing variable
Ideal gas
a gas that obeys the formula pV/T = constant
pressure
volume
temperature
Equation of state
pV = nRT
pressure x volume = number of moles x universal molar gas constant x temperature
pV = NkT
N is the number of molecules
k is the Boltzmann constant
Number of moles (n)
mass / molar mass
[g] / [g mol⁻¹]
n is the number of moles
N is the number of molecules
n x NA = moles to molecules
N / NA = molecules to moles
Pressure of an ideal gas
p = 1/3 (Nm/V)<c²>
or
pV = 1/3 . Nm . <c²> = NkT
1/3 . m . <c²> = kT
Nm is the mass of all the molecules of the gas hence Nm/V is density
p = 1/3ρ<c²>
Boltzmann constant
k = R/Nₐ
the gas constant per molecule, a fundamental constant
Kinetic energy of a molecule
Ek = 1/2 . m . <c²> = 3/2 kT
Root-mean-square speed
the square root of the average of the squares of the speeds of all the molecules in a gas
cᵣ.ₘ.ₛ = √<c²>
= √3KT/m
Electric field strength at a point
E = F / Q
electric field strength = force on charge / charge
the force per unit charge exerted on a stationary positive charge at that point
Strength of a uniform field between 2 parallel metal plates
E = ∆V / ∆d
E = Fe / q
Fe = qV / d
electric field strength = change in potential difference / change in distance
Newton’s universal gravitation law
force between 2 point masses is directly proportional to the product of the 2 masses and inversely proportional to the square of their centre to centre separation
Fg = GM1M2/r²
Force experienced by a point mass in a G-field
g = G . M/r² = a
Gravitational field strength
force per unit mass
GPE
work done in bringing the mass from infinity to the position in the gravitational fields
∆GPE = -GMm(1/r1 - 1/r2)
Orbital motion
Fc = Fg as centripetal force is provided by gravitational force
Orbital speed
Vorbit = √GM/r
T² = 4π²/GM . r³
T1²/r1³ = T2²/r2³
Total energy in orbital motion
-1/2 GMm/r
Escape speed
Vescape = √2GM/r
= √2gr
r = 2kQq/mv²
Electric field definition
a region of space where electric charges experience a force
Speed formula combined from electric and gravitation
v = √2g∆s
v = √2qV/m
Millikan’s experiment formulas
Fn = Fe
a = mg = qE
a = qV/md
q = mgd/V = ne
Electric potential energy formula
Work required to bring a point charge from infinity to a point
repulsive, EPE > 0
attractive, EPE < 0
EPE = Fe x r
k = Qq/r² . r
EPE = k . Qq/r²
Fe = k . Q1Q2/r
k = 1/4 . π ε₀
ε₀ is the permittivity of a vacuum
Electric field strength definition
force per unit positive charge acting on a point
E = F/q
V = kQ/r
∆V = kQ(1/r1 - 1/r2)
Capacitance
c = Q/V
Capacitors in parallel
C tot = C1 + C2 …
Capacitors in series
C tot = 1/C1 + 1/C2 … ⁻¹
Dielectric formula
c = ε₀εᵣ . A/d
Permittivity formulas
c = R/k = 4πε₀R
Arc length
rθ
Energy stored in capacitor
W = Q²/2C = 1/2cV² = 1/2QV
Grav and electric field formulas together
Force
Fg = GMm/r²
Fe = kQq/r²
Work done (Potential energy)
E = GMm/r
E = kQq/r
Field strength/force felt
g = GM/r²
E = kQ/r² (electric field strength not energy)
How much energy needed to move from infinity to point (potential)
V = –GM/r (V as in potential)
V = –kQ/r
g = ∆V/∆r
