Formulas to memorise** account for mid years tbc Flashcards
Newton’s second law (applied formula)
F = ma
force (N)
mass (kg)
acceleration (ms⁻²)
Change in pressure
∆p = ϱg∆h
pressure (Pa/Nm⁻²)
density (kgm⁻³)
gravitational acceleration (ms⁻²)
height (m)
Work done (in terms of pressure)
W = -p∆V
work (J/Nm)
pressure (Pa/Nm⁻²)
volume (m³)
Kinetic energy
Eₖ = 1/2mv²
kinetic energy (J)
mass (kg)
velocity (ms⁻¹)
Work done (in terms of force)
W = Fs
= Fr cosθ
work (J/Nm)
force (N)
displacement (m)
Change in gravitational potential energy
∆GPE = mg∆h
gravitational potential energy (J)
mass (kg)
gravitational acceleration (ms⁻²)
height (m)
Power (in terms of work)
P = W / t
power (Watt/Js⁻¹)
work done (J)
time (s)
Power (with constant velocity)
P = Fv
power (Watt/Js⁻¹)
force (N)
velocity (ms⁻¹)
Wave velocity
V = fλ
wave velocity (ms⁻¹)
frequency (Hz/s⁻¹)
wavelength (m)
Charge
Q = It
charge (c)
current (A)
time (s)
Potential difference (in terms of work)
V = W / Q
potential difference (volts) work done (energy/J) charge (c)
Power (in terms of voltage)
P = VI
power (Watt/Js⁻¹)
potential difference (volts)
current (A)
Power (in terms of resistance)
P = I²R
power (Watt/Js⁻¹)
current (A)
resistance (Ohms)
Potential difference (in terms of resistance)
V = IR
potential difference (volts)
current (A)
resistance (Ohms)
Resistance (in terms of resistivity)
R = ρL / A
resistance (Ohms)
resistivity (Ωm⁻¹)
length (m)
cross-sectional area (m²)
Density
ρ = m/V
density (kgm⁻³)
mass (kg)
volume (m³)
Pressure (in terms of area)
P = F/A
pressure (Pa/Nm⁻²)
force (N)
cross-sectional area (m²)
Spring constant
F = kx
force (N)
spring constant
x (m)
Kinematics equations not given
v = u + at s = { (u+v)/2 } x t
Net force in terms of momentum
Fₙ = ∆mv / ∆t or
= ∆p / ∆t
Net force (N) change in momentum (kg•m/s) time (s)
Momentum
p = mv
momentum (kgm⁻¹)
mass (kg)
velocity (ms⁻¹)
Impulse
Fₙ = (mv - mu)/t
∆momentum (p) = Fₙ x ∆t
Elastic force
F = -kx
force (N)
spring constant
x (m)
Weight
F = mg
force (N)
mass (kg)
gravitational acceleration (ms⁻²)
Torque (moment)
Torque (torque)
τ = F⊥ x r or τ = F x r⊥ or τ = Fr sinθ or τ = 2Fr
torque (Nm)
either perpendicular force (N) or perpendicular distance from pivot (m)
Efficiency ratio
useful energy output / total energy supplied
Net pressure (pressure at the bottom of a not fully submerged mass)
Pₙ = Pₒ + ϱg∆h
pressure (Pa/Nm⁻²) atmospheric pressure (101,000Pa) density (kgm⁻³) gravitational acceleration (ms⁻²) height (m)
Buoyancy formula
B = ϱg∆h•A or ϱgV
buoyancy (N) density (kgm⁻³) gravitational acceleration (ms⁻²) height (m) area (m²)
Archimedes principle (applied formula)
∆p = p₂ - p₁ = ϱg(h₂ - h₁)
Stress
σ = F/A
stress (Pa/Nm⁻²)
force (N)
area (m²)
Strain
ε = x/L
strain (no unit)
extension (m)
length (m)
Young’s modulus
E = σ / ε
or
E = FL / Ax
Young’s modulus (Pa/Nm⁻²)
stress (Pa/Nm⁻²)
strain (no unit)
Hooke’s Law in series
kᴛᴏᴛᴀʟ = (1/k1 + 1/k2 + 1/k3)⁻¹
Hooke’s Law in parallel
kᴛᴏᴛᴀʟ = k1 + k2 + k3
Velocity
V = ∆d / ∆t
velocity (ms⁻¹)
displacement (m)
time (s)
Acceleration
a = ∆v / ∆t
(area under graph is displacement)
acceleration (ms⁻²)
velocity (ms⁻¹)
time (s)
Elastic potential energy
Eₚ = 1/2 kx²
elastic potential energy (J)
spring constant
extension (m)
Elastic modulus
σε = energy / Volume
stress•strain (Pa/Nm⁻²)
energy (J)
Volume (m³)
Base Quantities and Units
Time (s) Mass (kg) Distance (m) Amount of substance (mol) Current (A) Temperature (K)
Newton’s first law of motion
an object will remain at rest or in a state of motion unless it is acted upon by a resultant force
Newton’s second law of motion
resultant force is proportional to rate change of momentum
Newton’s third law of motion
when 2 bodies interact, the forces they exert on each other are equal and opposite in size
Principle of conservation of momentum
in an isolated system, the total momentum of the masses before collision is equal to the total momentum of the masses after collision
Elastic Collisions
KE is conserved and rsa is equal to rss
Inelastic Collisions
KE after collision is lesser than KE before collision
Principle of moments
when in equilibrium, total clockwise moment about a point is equal to the total anticlockwise moment about that point
Conditions of equilibrium
sum of all force is equal to zero and sum of all clockwise moments is equal to the sum of all anticlockwise moments, there is no net force or resultant force
Principle of conservation of energy
Energy cannot be created or destroyed, only transformed
Archimedes’ Principle
Mass of a body submerged is equal to the mass of water it displaced
Wave period
T = 1/f
time (s)
frequency (Hz)