1
Q
The 4 kinematic equations of motion
A
- v = u + at
- s = ut + 1/2 at2
- v2 = u2 + 2as
- s = (u+v)t/2
Where:
* s = displacement (m)
* u = initial velocity (ms-1)
* v = final velocity (ms-1)
* a = acceleration (ms-2)
* t = time (s)
2
Q
Newton’s force equation
A
ΣF = ma
Where:
* ΣF = sum of forces (N)
* m = mass (kg)
* a = acceleration (ms-2)
3
Q
Simple gravitational field strength equation
A
g = F/m
Where:
* g = gravitational field strength (N kg-1 or ms-2)
* F = force (N)
* m = mass (kg)
4
Q
Weight equation
A
W = mg
Where:
* W = weight (N)
* m = mass (kg)
* g = gravitational field strength (N kg-1 or ms-2)
5
Q
Moment of a force equation
A
moment = Fx
Where:
* F = force (N)
* x = perpendicular distance to the pivot from the line of action of the force (m)
6
Q
Momentum equation
A
p = mv
Where:
* p = momentum (kgms-1)
* m = mass (kg)
* v = velocity (ms-1)
7
Q
Mechanical work done equation
A
∆W = F∆s
Where:
* ∆W = work done (J)
* F = force (N)
* s = displacement (m)
8
Q
Kinetic energy equation
A
EK = 1/2 mv2
Where:
* EK = kinetic energy (J)
* m = mass (kg)
v = velocity (ms-1)
9
Q
Simple gravitational potential energy equation
A
∆Egrav = mg∆h
Where:
* ∆Egrav = gravitational potential energy (J)
* m = mass (kg)
* g = gravitational field strength (N kg-1 or ms-2)
10
Q
Mechanical power equation
A
P = W/t
Where:
* P = power (W)
* W = work done (J)
* t = time (s)
11
Q
General power equation
A
P = E/t
Where:
* P = power (W)
* E = energy (J)
* t = time (s)
12
Q
Power efficiency equation
A
efficiency = (useful power output)/(total power input)
13
Q
Energy efficiency equation
A
efficiency = (useful energy output)/(total energy input)
14
Q
Potential difference equation
A
V = W/Q
Where:
* V = potential difference (V)
* W = work done (J)
* Q = charge (C)
15
Q
Ohm’s law
Resistance equation
A
R = V/I
Where:
* R = resistance (Ω)
* V = potential difference (V)
* I = current (A)
16
Q
Electrical power equation using current and potential difference
A
P = VI
Where:
* P = electrical power (W)
* V = potential difference (V)
* I = current (A)
17
Q
Electrical power equation using current and resistance
A
P = I2R
Where:
* P = electrical power (W)
* I = current (A)
* R = resistance (Ω)
18
Q
Electrical power equation using potential difference and resistance
A
P = V2/R
Where:
* P = electrical power (W)
* V = potential difference (V)
* R = resistance (Ω)
19
Q
Electrical energy equation
A
W = Pt
Where:
* W = work done (J)
* P = power (W)
* t = time (s)
20
Q
Resistivity equation
A
R = ρl/A
Where:
* R = resistance (Ω)
* ρ = resistivity (Ω m)
* l = length (m)
* A = cross-sectional area (m2)
21
Q
Current equation involving time
A
I = ∆Q/∆t
Where:
* I = current (A)
* Q = charge (C)
* t = time (s)
22
Q
Current equation involving cross-sectional area
A
I = nAvq
Where:
* I = current (A)
* n = number of free charge carriers per unit volume (m-3)
* A = cross-sectional area (m2)
* v = average drift velocity (ms-1)
* q = charge of each carrier (C)
23
Q
Density equation
A
ρ = m/V
Where:
* ρ = density (kgm-3)
* m = mass (kg)
V = volume (m3)
24
Q
Stokes’ law equation
A
F = 6πηrv
Where:
* F = viscous drag force (N)
* η = fluid viscosity (Pa s or kgm-1s-1)
* r = radius of spherical object (m)
* v = velocity of spherical object (ms-1)
25
**Simple** equation for Hooke's law
∆F = k∆x
Where:
* ∆F = restoring force (N)
* k = spring constant (Nm-1)
* ∆x = spring extension/compression (m)
26
Stress equation
σ = F/A
Where:
* σ = stress (Pa **or** Nm-2)
* F = applied force (N)
* A = cross-sectional area (m2)
27
Strain equation
ε = ∆x/x
Where:
* ε = strain (no units)
* ∆x = extension (m)
* x = original length (m)
28
Young modulus equation
E = σ/ε
Where:
* E = young modulus (Pa **or** Nm-2)
* σ = stress (Pa **or** Nm-2)
* ε = strain (no units)
29
Elastic strain energy equation
∆Eel = 1/2 F∆x
Where:
* ∆Eel = elastic potential energy (J)
* F = applied force (N)
* ∆x = extension/compression (m)
30
Wave speed equation
v = fλ
Where:
* v = wave speed (ms-1)
* f = frequency (Hz)
* λ = wavelength (m)
31
Speed of a transverse wave on a string equation
v = √(T/μ)
Where:
* v = wave speed (ms-1)
* T = tension (N)
* μ = linear density (kgm-1)
32
Linear mass density equation
μ = m/L
Where:
* μ = linear mass density (kgm-1)
* m = mass (kg)
* L = length (m)
33
Intensity of radiation equation
I = P/A
Where:
* I = intensity (Wm-2)
* P = power (W)
* A = surface area (m2)
34
Lens power equation using **focal length**
P = 1/f
Where:
* P = power of lens / optical power (D **or** m-1)
* f = focal length (m)
35
Lens power equation using **optical powers**
Ptotal = P1 + P2 + P3 ...
Where:
* Ptotal = total power (D **or** m-1)
* P1 = optical power of lens 1 (D **or** m-1)
* P2 = optical power of lens 2 (D **or** m-1)
* P3 = optical power of lens 3 (D **or** m-1)
36
Thin lens equation
1/u + 1/v = 1/f
Where:
* u = object distance (m)
* v = image distance (m)
* f = focal length (m)
37
Lens magnification equation
m = v/u
Where:
* m = magnification (no units)
* v = image height (m)
* u = object height (m)
38
Diffraction grating equation
nλ = dsinθ
Where:
* n = order of maximum integer (no units)
* λ = wavelength of incident light (m)
* d = slit spacing/separation (m)
* θ = the angle between the normal and the direction of the maximum (º)
39
Refractive index equation using **trigonometry**
n1 sinθ1 = n2 sinθ2
Where:
* n1 = refractive index of the first medium (the material the light is coming from)
* θ1 = the angle of incidence (between the incoming light ray and the normal before it enters a second medium)
* n2 = refractive index of the second medium (the material the light is entering)
* θ2 = the angle of refraction (between the light ray and the normal after it has entered the second medium)
40
Refractive index equation using **speed of light**
n = c/v
Where:
* n = absolute refractive index of the material (no units)
* c = speed of light in a vacuum (3 x 108 ms-1)
* v = speed of light through the material (ms-1)
41
Critical angle equation
sin C = 1/n
Where:
* C = critical angle (the angle of incidence in a dense medium for which the angle of refraction in the less dense medium is exactly 90º)
* n = refractive index (no units)
42
Photon model equation
E = hf
Where:
* E = energy of the photon (J **or** eV)
* h = Planck's constant (6.63 x 10-34 Js)
* f = frequency of the EM radiation (Hz)
43
Einstein's photoelectric equation
hf = Φ + 1/2 mv2max
Where:
* h = Planck's constant (6.63 x 10-34 Js)
* f = frequency of the EM radiation (Hz)
* Φ = work function / the minimum energy required for the emission of an electron from the surface of a material (J **or** eV)
* m = mass of electron (9.11 x 10-31 kg)
* vmax = maximum velocity of the ejected photon (ms-1)
44
de Broglie wavelength equation
λ = h/p
Where:
* λ = de Broglie wavelength / particle wavelength (m)
* h = Planck's constant (6.63 x 10-34 Js)
* p = momentum of the particle (kgms-1)
45
Impulse equation
∆p = F∆t
Where:
* ∆p = impulse / change in momentum (kgms-1)
* F = average force (N)
* t = duration for which the force is applied (s)
46
Kinetic energy of a **non-relativistic** particle equation
EK = p2/2m
Where:
* EK = kinetic energy (J)
* p = linear momentum of particle (kgms-1)
* m = mass of particle (kg)
47
Equation for the relationship between linear and angular velocity
v = ωr
Where:
* v = instantaneous linear velocity (ms-1)
* ω = angular velocity (rad s-1)
* r = radius of orbit (m)
48
Equation for time period involving **angular velocity**
T = 2π/ω
Where:
* T = time taken for one complete cycle of motion (s)
* 2π = full circle in radians
* ω = angular velocity (rad s-1)
49
Equation for angular velocity involving **frequency**
ω = 2πf
Where:
* ω = angular velocity (rad s-1)
* 2π = full circle in radians
* f = frequency / the number of cycles per second (Hz **or** s-1)
50
Equation for centripetal force including **linear velocity**
F = mv2/r
Where:
* F = centripetal force (N)
* m = mass (kg)
* v = instantaneous linear velocity (ms-1)
51
Equation for centripetal force including **angular velocity**
F = mrω2
Where:
* F = centripetal force (N)
* m = mass (kg)
* r = radius of orbit (m)
* ω = angular velocity (rad s-1)
52
Centripetal acceleration equation with **linear velocity**
a = v2/r
Where:
* a = centripetal acceleration (ms-2)
* v = linear velocity (ms-1)
* r = radius of orbit (m)
53
Centripetal acceleration equation with **angular velocity**
a = rω2
Where:
* a = centripetal acceleration (ms-2)
* r = radius of orbit (m)
* ω = angular velocity (rad s-1)
54
Coulomb's law equation
F = Q1Q2/4πε0r2
Where:
* F = electrostatic force (N)
* Q1 & Q2 = point charges (C)
* 1/4πε0 = Coulomb's constant, k (8.99 x 109 Nm2 C-2)
* ε0 = permittivity of free space (8.85 x 10-12 F m-1)
* r = distance between the point charge centres (m)
55
Electric field strength equation involving **force**
E = F/Q
Where:
* E = electric field strength (NC-1)
* F = electrostatic force (N)
* Q = charge (C)
56
Electric field strength equation involving **Coulomb's law**
E = Q/4πε0r2
Where:
* E = electric field strength (NC-1)
* Q = charge (C)
* 1/4πε0 = Coulomb's constant, k (8.99 x 109 Nm2 C-2)
* ε0 = permittivity of free space (8.85 x 10-12 F m-1)
* r = distance between the point charge centres (m)
**OR**
E = kQ/r2
Where:
* k = Coulomb's constant, 1/4πε0 (8.99 x 109 Nm2 C-2)
57
Electric field strength equation involving **potential difference**
E = V/d
Where:
* E = electric field strength (Vm-1)
* V = potential difference between two points (V)
* d = parallel distance between two points (m)
58
Electric potential equation
V = Q/4πε0r
Where:
* V = electric potential (V)
* Q = charge (C)
* 1/4πε0 = Coulomb's constant, k (8.99 x 109 Nm2 C-2)
* ε0 = permittivity of free space (8.85 x 10-12 F m-1)
* r = distance between the point charge centres (m)
**OR**
V = kQ/r
Where:
* k = Coulomb's constant, 1/4πε0 (8.99 x 109 Nm2 C-2)
59
Capacitance equation
C = Q/V
Where:
* C = capacitance (F)
* Q = charge on one of the capacitor plates (C)
* V = potential difference between the plates (V)
60
Equation for energy stored in a capacitor involving **charge** and **potential difference**
W = 1/2 QV
Where:
* W = electric potential energy stored (J)
* Q = charge on one of the capacitor plates (C)
* V = potential difference between the plates (V)
61
Equation for energy stored in a capacitor involving **capacitance** and **potential difference**
W = 1/2 CV2
Where:
* W = electric potential energy stored (J)
* C = capacitance (F)
* V = potential difference between the plates (V)
62
Equation for energy stored in a capacitor involving **capacitance** and **charge**
W = Q2/2C
Where:
* W = electric potential energy stored (J)
* Q = charge on one of the plates (C)
* C = capacitance (F)
63
Equation for the exponential **discharge** of a capacitor
Q = Q0e-t/RC
Where:
* Q = an instantaneous charge on the capacitor at time t (C)
* Q0 = the initial charge on the capacitor at time 0 (C)
* e = the base of the natural logarithm (roughly 2.718)
* t = the elapsed time since discharge began (s)
* R = resistance (Ω)
* C = capacitance (F)
* RC = time constant, τ (when t = RC, the charge Q drops to approximately 37%, 1/e, of the initial charge Q0)
64
Equation for the exponential decay of **current** in a resistor-capacitor (RC) circuit
I = I0e-t/RC
Where:
* I = an instantaneous current flowing through the circuit at time t (A)
* I0 = the initial current on the capacitor at time 0 (A)
* e = the base of the natural logarithm (roughly 2.718)
* t = the elapsed time since discharge began (s)
* R = resistance (Ω)
* C = capacitance of the capacitor (F)
* RC = time constant, τ (when t = RC, the current I drops to approximately 37%, 1/e, of the initial current I0)
65
Equation for the exponential decay of **potential difference** in a resistor-capacitor (RC) circuit
V = V0e-t/RC
Where:
* V = an instantaneous voltage flowing through the circuit at time t (V)
* V0 = the initial voltage on the capacitor at time 0 (V)
* e = the base of the natural logarithm (roughly 2.718)
* t = the elapsed time since discharge began (s)
* R = resistance (Ω)
* C = capacitance of the capacitor (F)
* RC = time constant, τ (when t = RC, the voltage V drops to approximately 37%, 1/e, of the initial voltage V0)
66
Equation for the **linear exponential decay** for the **discharge** of a capacitor
ln(Q) = (lnQ0) - t/RC
Where:
* ln(Q) = natural logarithm of the instantaneous charge on the capacitor at time t (C)
* ln(Q0) = natural logarithm of the initial charge on the capacitor at time 0 (C)
* t = the elapsed time since discharge began (s)
* R = resistance (Ω)
* C = capacitance of the capacitor (F)
* RC = time constant, τ (when t = RC, the charge Q drops to approximately 37%, 1/e, of the initial charge Q0)
* -1/RC = gradient for a graph of ln(Q) - time t
67
Equation for the **linear exponential decay** for the **current** in a resistor-capacitor (RC) circuit
ln(I) = ln(I0) - t/RC
Where:
* ln(I) = natural logarithm of the instantaneous current in the circuit at time t (A)
* ln(I0) = natural logarithm of the initial current in the circuit at time 0 (A)
* t = the elapsed time since discharge began (s)
* R = resistance (Ω)
* C = capacitance of the capacitor (F)
* RC = time constant, τ (when t = RC, the current I drops to approximately 37%, 1/e, of the initial current I0)
* -1/RC = gradient for a graph of ln(I) - time t
68
Equation for the **linear exponential decay** for the **potential difference** in a resistor-capacitor (RC) circuit
ln(V) = ln(V0) - t/RC
Where:
* ln(V) = natural logarithm of the instantaneous voltage in the circuit at time t (V)
* ln(V0) = natural logarithm of the initial voltage in the circuit at time 0 (V)
* t = the elapsed time since discharge began (s)
* R = resistance (Ω)
* C = capacitance of the capacitor (F)
* RC = time constant, τ (when t = RC, the voltage V drops to approximately 37%, 1/e, of the initial voltage V0)
* -1/RC = gradient for a graph of ln(V) - time t
69
Force in a magnetic field equation involving **current**
F = BILsinθ
Where:
* F = magnetic force exerted on the wire (N)
* B = magnetic flux density (T **or** Wbm-2)
* I = current (A)
* L = length of the conductor (m)
* θ = angle between direction of the current and the external magnetic flux lines (º)
70
Force in a magnetic field equation involving **charge**
F = BQvsinθ
Where:
* F = magnetic force exerted on the charged particle (N)
* B = magnetic flux density (T **or** Wbm-2)
* Q = charge of the particle (C)
* v = velocity of the particle as it moves through the field (ms-1)
* θ = angle between the direction of the velocity vector and the magnetic field vector (º)
71
Faraday's and Lenz's law equation
ε = -d(NΦ)/dt
Where:
* ε = induced electromotive force, emf (V)
* d = an instantaneous change (rather than ∆ which shows an average change)
* N = number of turns in the coil of wire (no units)
* Φ = magnetic flux passing through a single loop of the coil (Wb)
* t = time (s)
72
Root-mean-square equation for **potential difference**
Vrms = V0/√2
Where:
* Vrms = root mean square voltage (V)
* V0 = peak voltage (V)
73
Root-mean-square equation for **current**
Irms = I0/√2
Where:
* Irms = root mean square current (A)
* I0 = peak current (A)
74
Equation for the perpendicular motion of a charged particle in a unifrom magnetic field
r = p/BQ
Where:
* r = radius of orbit (m)
* p = momentum of the charged particle (kgms-1 **or** Ns)
* B = magnetic field strength, magnetic flux density (T **or** Wbm-2)
* Q = charge of the particle (C)
75
Specific heat capacity equation
∆E = mc∆θ
Where:
* ∆E = change in thermal energy (J)
* m = mass of the substance (kg)
* c = specific heat capacity (J kg-1 K-1 **or** J kg-1 ºC-1)
* ∆θ = change in temperature (K **or** ºC)
76
Specific latent heat equation
∆E = L∆m
Where:
* ∆E = change in energy (J)
* L = latent heat (J kg-1)
* ∆m = change in mass, the mass defect/gain (kg)
77
Equation for the average kinetic energy of a single particle in an ideal gas in thermal equilibrium
1/2 m(c2) = 3/2 kT
Where:
* m = mass of a single particle (kg)
* (c2) = root mean square speed of the particles (m2 s-2)
* k = Boltzmann constant (1.38 x 10-23 JK-1)
* T = absolute temperature of the gas (K)
78
Kinetic theory of gases equation
pV = 1/3 Nm(c2)
Where:
* p = pressure of the gas (Pa **or** Nm-2)
* V = volume of the container holding the gas (m3)
* N = total number of molecules/atoms in the gas (no units)
* m = mass of a single molecule (kg)
* (c2) = root mean square speed of the gas molecule (m2 s-2)
79
Ideal gas equation
pV = NkT
Where:
* p = pressure of the gas (Pa **or** Nm-2)
* V = volume of the container holding the gas (m3)
* N = total number of molecules/atoms in the gas (no units)
* k = Boltzmann constant (1.38 x 10-23 J K-1)
* T = absolute temperature (K)
80
Equation for Stefan-Boltzmann law involving the **surface area** of a **substance**
L = σAT4
Where:
* L = luminosity (W **or** Js-1)
* σ = Stefan-Boltzmann constant (5.67 x 10-8 Wm-2 K-4)
* A = total surface area of the emitting substance (m2)
* T = absolute temperature (K)
81
Equation for Stefan-Boltzmann law involving the **surface area** of a **spherical object**
L = 4πr2σT4
Where:
* L = luminosity (W **or** Js-1)
* 4πr2 = surface area of a sphere (m2)
* σ = Stefan-Boltzmann constant (5.67 x 10-8 Wm-2 K-4)
* T = absolute temperature (K)
82
Wien's law equation
λmaxT = b
Where:
* λmax = peak wavelength (m)
* T = absolute temperature (K)
* b = Wien's displacement constant (2.898 × 10-3 m K)
83
Inverse square law equation for **light intensity**
I = L/4πd2
Where:
* I = radiant flux intensity, apparent brightness (W m-2)
* L = luminosity of the light source (W)
* d = distance from the observer to the light source, radius (m)
* 4πd2 = surface area of a sphere (m2)
84
Non-relativistic **Doppler effect** equation
z ≈ ∆λ/λ ≈ ∆f/f ≈ v/c
Where:
* z = redshift when z > 0, blueshift when z < 0 (no units)
* ∆λ = difference between the observed and emitted wavelength (m)
* λ = original wavelength of the source (m)
* ∆f = difference between the observed and emitted frequency (Hz)
* f = original frequency of the source (Hz)
* v = relative velocity (ms-1)
* c = speed of light (3 x 108 ms-1)
85
Hubble's law equation
v = H0d
Where:
* v = recessional velocity of a galaxy (kms-1)
* H0 = Hubble constant (67.4 ± 0.5 kms-1 Mpc-1) (kilometres per second per megaparsec)
* d = the distance to the galaxy (Mpc)
86
Mass-energy equation
∆E = c2∆m
Where:
* ∆E = change in total energy of the system (J)
* c2 = squared speed of light (9 x 1016 m2 s-2)
* ∆m = change in mass of the system (kg)
87
Radiation activity equation
A = λN
Where:
* A = activity, the number of nuclear decays per unit time (Bq = 1 decay per second)
* λ = decay constant (s-1)
* N = total number of radioactive nuclei remaining in the sample (no units)
88
**Radioactive decay** equation
dN/dt = -λN
Where:
* N = the amount of substance or indivudals remaining at time t (no units)
* t = elapsed time since decay began (s)
* λ = decay constant (s-1)
* dN/dt = the rate of decrease in N
* Negative symbol = represents that N is **decaying**
89
Equation for the relationship between the **decay constant** and the **half-life**
λ = ln(2)/t1/2
Where:
* λ = decay constant (s-1)
* ln(2) = the natural logarithm of 2, roughly 0.693 (used mathematically when solving the exponential decay equation for the point where the substance is reduced to exactly half (50%) of its initial amount)
* t1/2 = the half-life of the substance, the amount of time required for half of a samples radioactive nuclei to undergo decay
90
Exponential decay equation for the **number of radioactive nuclei**
N = N0e-λt
Where:
* N = the number of radioactive nuclei remaining at time t (s)
* N0 = initial number of radioactive nuclei at time 0 (s)
* e = the base of the natural logarithm (roughly 2.718)
* λ = decay constant (s-1)
* t = elapsed time since decay began (s)
91
Exponential decay equation for the **activity of radioactive nuclei**
A = A0e-λt
Where:
* A = the activity of the substance at time t (s)
* A0 = the initial activity of the substance at time 0 (s)
* e = the base of the natural logarithm (roughly 2.718)
* λ = decay constant (s-1)
* t = elapsed time since decay began (s)
92
Gravitational force equation
F = Gm1m2/r2
Where:
* F = gravitational force between the two objects (N)
* G = universal gravitational constant (6.67 x 10-11 Nm2 kg-2)
* m1 & m2 = point masses (kg)
* r = distance between the centres of the point masses (m)
93
**Advanced** gravitational field strength equation
g = GM/r2
Where:
* g = gravitational field strength (ms-2)
* G = universal gravitational constant (6.67 x 10-11 Nm2 kg-2)
* M = mass of the large body, e.g. planet or star (kg)
* r = distance from the centre of the large body to the point where gravity is being measured (m)
94
Gravitational potential equation
Vgrav = -GM/r
Where:
* Vgrav = gravitational potential (J kg-1)
* G = universal gravitational constant (6.67 x 10-11 Nm2 kg-2)
* M = mass of the large body, e.g. planet or star (kg)
* r = distance from the centre of the large body to the point where gravity is being measured (m)
* Negative sign = gravity is attractive, so work must be done against the field to move an object away, therefore the **potential is always negative at any finite distance**. The **potential is defined as zero at an infinite distance**.
95
**Advanced** gravitational potential energy equation
Egrav = -GMm/r
Where:
* Egrav = gravitational potential energy (J)
* G = universal gravitational constant (6.67 x 10-11 Nm2 kg-2)
* M = mass of object 1, the larger object (kg)
* m = mass of object 2, the smaller object (kg)
* r = distance between the centres of mass of the two objects (m)
* Negative sign = indicates gravity is an attractive force. Potential energy is defined as zero at an infinite distance, and as objects move closer together, their potential energy decreases (becomes more negative)
96
# For simple harmonic motion
**Advanced** equation for Hooke's law
F = -kx
Where:
* F = restoring force, the force exerted by the spring to return to its original position (N)
* k = spring constant (Nm-1)
* x = the distance that the spring has been stretched or compressed from its equilibrium position (m)
* Negative sign = an indication the the restoring force F is always in the opposite direction of displacement (e.g. if you pull a spring vertically down, the restoring force will act vertically up)
97
Equation for the acceleration of an object in simple harmonic motion
a = -ω2x
Where:
* a = acceleration of the object/particle (ms-2)
* ω = angular frequency (rad s-1)
* x = displacement from the equilibrium position (m)
98
Equation that describes the displacement of a system in simple harmonic motion that starts at its positive maximum displacement at time 0
x = A cos(ωt)
Where:
* x = displacement, the distance of the object from its equilibrium position at a given time t (m)
* A = amplitude, the maximum displacement from the equilibrium position (m)
* ω = angular frequency (rad s-1)
* t = elapsed time since the motion began (s)
99
Equation that represents the instantaneous velocity of an object undergoing simple harmonic motion, when displacement is defined as x = A cos(ωt)
v = −Aω sin(ωt)
Where:
* v = instantaneous velocity of the object at a given time t (ms-1)
* A = amplitude, the maximum displacement from the equilibrium position (m)
* ω = angular frequency (rad s-1)
* t = elapsed time since the motion began (s)
* Negative sign = the velocity vector is in the opposite direction of displacement when the object is moving away from the equilibrium point
100
Equation that represents the instantaneous acceleration of an object undergoing simple harmonic motion, when velocity is defined as v = −Aω sin(ωt)
a = -Aω2 cos(ωt)
Where:
* a = instantaneous acceleration of the object at a given time t (ms-2)
* A = amplitude, the maximum displacement from the equilibrium position (m)
* ω = angular frequency (rad s-1)
* t = elapsed time since the motion began (s)
* Negative sign = acceleration is a restoring quantity and always points back towards the equilibrium position (opposite to the direction of displacement)
## Footnote
This equation assumes the object started at maximum positive displacement at time t = 0
101
Equation for the period of a mass-spring system in **simple harmonic motion**
T = 2π √(m/k)
Where:
* T = duration of time for the system to complete one full cycle of motion (s)
* m = mass attached to the spring (kg)
* k = spring constant (Nm-1)
102
Equation for the period of a **simple pendulum** undergoing small-angle oscillations
T = 2π √(l/g)
Where:
* T = duration of time for the system to complete one full back-and-forth cycle (s)
* l = length from the pivot point to the centre of mass of the pendulum bob (m)
* g = gravitational field strength (ms-2)
103
**Instantaneous** power equation
P = Fv
Where:
* P = instantaneous power (W)
* F = force (N)
* v = velocity (ms-1)
104
Wave **phase difference** equation
∆Φ = 2π∆x/λ
Where:
* Φ = phase difference (radians **or** º)
* ∆x = path difference, the difference in distance travelled by two waves **or** the distance between two points on the same wave (m)
* λ = wavelength (m)
105
Wave **path difference** equation for **constructive** interference
∆x = nλ
Where:
* ∆x = path difference, the difference in distance travelled by two waves **or** the distance between two points on the same wave (m)
* n = order number, an integer that represents the order of the interference maximum/fringe (n = 0: central maximum, n = 1: first order where ∆x = λ, n = 2: second order where ∆x = 2λ, etc.)
* λ = wavelength of the monochromatic wave source (m)
106
Wave **path difference** equation for **destructive** interference
∆x = (n + 1/2)λ
Where:
* ∆x = path difference, the difference in distance travelled by two waves **or** the distance between two points on the same wave (m)
* n = order number, an integer that represents the order of the interference maximum/fringe (n = 0: central maximum, n = 1: first order where ∆x = λ, n = 2: second order where ∆x = 2λ, etc.)
* λ = wavelength of the monochromatic wave source (m)
* (n + 1/2) = ensures that the path difference is an odd half-integer multiple of the wavelength, which is required for out-of-phase waves
107
Stationary wave equation
L = nλ/2
Where:
* L = length of the string (m)
* n = harmonic number, an integer that identifies the mode of vibration (**n = 1: fundamental frequency**/first harmonic - simplest standing wave pattern, **n = 2: second harmonic** etc.)
* λ = wavelength (m)
* 2 = half of a full wave length represents a single loop in a standing wave
108
Orbital speed in gravitational fields equation
v = √(GM/r)
Where:
* v = orbital speed (ms-1)
* G = universal gravitational constant (6.67 x 10-11 Nm2 kg-2)
* M = mass of large body (kg)
* r = radius of orbit (m)
109
Work done in an electric field equation
W = QV
Where:
* W = work done (J)
* Q = charge (C)
* V = potential difference (V)
110
Equation for the electric force exerted on a charged particle in an electric field
F = EQ
Where:
* F = electrostatic force (N)
* E = electric field strength (NC-1)
* Q = electric charge (C)
111
Magnetic flux equation
Φ = BAcosθ
Where:
* Φ = magnetic flux (Wb)
* B = magnetic flux density, also called magnetic field strength (T)
* A = cross-sectional area of surface/coil (m2)
* θ = angle between the magnetic field lines and the normal (º)
112
Magnetic flux linkage equation
NΦ = BANcosθ
Where:
* NΦ = magnetic flux linkage, the product of the numbers of turns and the flux through each turn (Wb-turns)
* B = magnetic flux density, magnetic field strength (T)
* A = cross-sectional area of the coil (m2)
* N = number of turns in a coil
* θ = angle between the magnetic field and the normal (º)
113
Equation for the maximum frictional force acting between two surfaces
F = μR
Where:
* F = frictional force (N)
* μ = coefficient of friction (material roughness), a number that tells you how easily one object will slide over another (no units)
* R = normal reaction force, exterted by a surface perpendicular to a force (N)
A-Level Physics Edexcel Flashcards
flashcards
Decks in class (15)
# Cards
-
Topic 1 - Working as a Physicist120
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Topic 2 - Mechanics136
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Topic 3 - Electricity152
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Topic 4 - Materials74
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Topic 5 - Waves & Particle Nature of Light201
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Topic 6 - Further Mechanics71
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Topic 7 - Electric & Magnetic Fields217
-
Topic 8 - Nuclear/Particle Physics190
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Topic 9 - Thermodynamics92
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Topic 10 - Space79
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Topic 11 - Nuclear Radiation64
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Topic 12 - Gravitational Fields60
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Topic 13 - Oscillations61
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Command Words2
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Equations113
