Formulas Flashcards
Arc length
s = rθ
(s) arc length [m]
(r) radius of circle [m]
(θ) angular displacement [rad]
Angular speed
ω = ∆θ / ∆t
(ω) angular speed [rad s⁻¹]
(θ) angular displacement [rad]
(t) time taken [s]
Angular speed equation for one revolution
ω = 2π / T
(ω) angular speed [rad s⁻¹]
(2π) angle rotated through by object in one revolution [rad]
(T) period/time to make one revolution [s]
Equation relating speed and angular speed
v = ωr
(v) speed [ms⁻¹]
(ω) angular speed [rad s⁻¹]
(r) radius [m]
Acceleration equations in circular motion (2)
a = v²/r or a = ω²r
(a) acceleration [ms⁻²]
(v) speed [ms⁻¹]
(r) radius [m]
(ω) angular velocity [rad s⁻¹]
Combining Newton’s second law and acceleration equations in circular motion
F = ma
a = v²/r or a = ω²r
∴
Fc = mv²/r or mω²r
(F) force [N]
(a) acceleration [ms⁻²]
(v) speed [ms⁻¹]
(r) radius [m]
(ω) angular velocity [rad s⁻¹]
(Fc) centripetal force [N]
(m) mass [kg]
Calculating orbital speed
F = ma
F = mv²/r
∴
ma = mv²/r
a = v²/r
(F) force [N]
(m) mass [kg]
(a) acceleration [ms⁻²]
(v) speed [ms⁻¹]
(r) radius [m]
Angular frequency equation
ω = 2πf
(ω) angular frequency [rad s⁻¹]
(f) frequency [Hz]
Equations of s.h.m
x = x₀sin ωt or x = x₀cos ωt
sine version used when x (displacement curve) = 0 at t = 0
cosine version used when x (displacement curve) = x₀ at t = 0
(x) displacement [m]
(x₀) max displacement [m]
(ω) angular frequency [rad s⁻¹]
(t) time [s]
Acceleration and displacement formula s.h.m
a = -ω²x
(a) acceleration [ms⁻²]
(ω) angular frequency [rad s⁻¹]
(x) displacement [m]
Equation for velocity in s.h.m
v = v₀cos ωt
cosine version used as the velocity is at a maximum when t = 0
(v) velocity [ms⁻¹]
(v₀) max velocity [ms⁻¹]
(ω) angular frequency [rad s⁻¹]
(t) time [s]
Speed of an oscillator (2)
v = (±)ω √x₀² - x²
v₀ = ωx₀
(v) velocity [ms⁻¹]
(ω) angular frequency [rad s⁻¹]
(x₀) max displacement [m]
(x) displacement [m]
(v₀) max velocity [ms⁻¹]
Total energy of a system undergoing s.h.m
E = 1/2mv₀² and v₀ = ωx₀
∴
E = 1/2mω²x₀²
(E) maximum kinetic energy and total energy of system [J]
(m) mass [kg]
(v₀) max velocity [ms⁻¹]
(ω) angular frequency [rad s⁻¹]
(x₀) max displacement [m]
Internal energy
∆U = q + w
(U) increase in internal energy [J]
(q) energy supplied by heating [J]
(w) work done on the system [J]
Work done when the volume of a gas changes at constant pressure
F = p x A
W = F x d
∴
W = p∆V
(F) force [N]
(p) pressure [kgm⁻³]
(A) area [m²]
(W) work done [J]
(V) volume [m³]
Note:
true if gas is expanding against pressure of atmosphere which changes only very slowly
Conversion between celsius and kelvin
θºC = T (K) - 273.15
T(K) = θºC + 273.15
(θ) temperature in ºC
(T) temperature in K
Specific heat capacity (2)
E = mc∆θ or Q = mc∆T
or
specific heat capacity = energy supplied / mass temperature change
(E) energy supplied [J]
(m) mass [kg]
(c) specific heat capacity [Jkg⁻¹ºC⁻¹]
(θ) temperature [ºC]
(Q) thermal energy supplied [J]
(T) temperature [K]
Energy formula involving power
E = p x t
(E) energy [J]
(p) power [W]
(t) time [s]
Specific latent heat (2)
E = mL or Q = mL
or
specific latent heat = rate of supply of energy / rate of loss of mass
(E) energy required to melt or vapourise [J]
(m) mass [kg]
(L) specific latent heat [Jkg⁻¹]
(Q) thermal energy required to melt or vapourise [J]
Number of atoms in specific mass of a substance
number of atoms in a substance
specific mass of substance / mass of a single atom of that substance
Number of moles (2)
For a specific mass of a substance:
number of atoms in a specific weight of the substance / avogadro constant
Given molar mass:
mass / molar mass
Boyle’s law
pV = constant
p₁V₁ = p₂V₂
(p) pressure [kgm⁻³]
(V) volume [m³]
Charles’ law
V/T = constant
V₁/T₁ = V₂/T₂
(V) volume [m³]
(T) temperature [K]
Key equation for fixed mass of gas
pV/T = constant
p₁V₁/T₁ = p₂V₂/T₂
(p) pressure [kgm⁻³]
(V) volume [m³]
(T) temperature [K]
