Download Formulae list - schoolphysics

Formulae list
Some of these formulae should be memorised during your higher level course but the list covers
a great deal more than is needed for a simple extension to the foundation course. It is most
important that you are sure of the meaning of all the symbols
Equations of motion
s = vt
v = u + at
v2 = u2 + 2as
s = ut + ½ at2
average vel. = [u + v]/2
Momentum
M = mv
Impulse
I = Ft
Newton’s second law F = d(mv)/dt = ma
Impulse and momentum
Ft = mv – mu
Kinetic energy
k.e = ½ mv2
Potential energy
p.e = mgh
Work
work = Fs
Power
Power = Fv
Weight
F = mg
Pressure
Pressure = F/A
Pressure in a liquid
Pressure = hg
Density
 = m/V
Couple
couple = Fd
Upthrust
U = vg
Projectiles
Range
Range = u2sin2A/g
Maximum height
h = u2sin2A/2g
Time of flight
t = 2usinA/g
Motion in a circle
Angular velocity
/t
Linear and angular velocity
v = r
Time of rotation period
T = 2r/v = 2/
Centripetal force
F = mv2/r = m2r
Rotational dynamics
Moment of inertia
I = mr2
Angular momentum M = I
Rotational k.e.
k.e = ½ I2
Couple
C = I
Work done
W = C
Simple harmonic motion
Acceleration
a = -2 x
Displacement
x =rsin(t)
Velocity
v = ±  (r2 - x2)1/2
Acceleration
a = -2 rsin(t)
Velocity
v = r cos (t)
Kinetic energy
k.e = ½ m2(r2 - x2)
Potential energy
p.e = ½ m2x2
Total energy
E = ½ m2r2
Gravitation
Kepler’s third law
T2/r3 = constant
Newton’s law
F = Gm1m2/d2
Potential energy
p.e = - GmM/r
Kinetic energy
k.e = +GmM/2r
Total energy
E = - GmM/2r
Potential
VG = - GM/r
go and G
go = GM/R2
g and go (r> R)
g = goR2/r2
g and go (r < R)
g = gor/R
Escape velocity
v = [2Rgo]1/2
Elasticity
Stress
stress = F/A
Strain
strain = e/L
Young modulus
E = F/LeA
Bulk modulus
K = p/(v/v)
Rigidity or shear modulus (G)
G = [F/A]/
p.e. stored
p.e. = ½ Fe = ½ EAe2/L
Energy per unit volume
energy = ½ stress x strain
Thermal expansion
F = EA
Coefficient of friction ()
F = R
Viscosity
Coefficient of viscosity ()
F = A x velocity gradient
Stokes’ law
F = 6rv
Poiseuille’s formula
Volume s-1 = hgr4/8l
Surface tension
Capillary rise (h)
T cos  = hrg/2
Excess pressure in air bubble
p = 2T/r
Excess pressure in soap bubble p = 4T/r
Geometrical Optics
Refractive index
n = sin i/sin r
n = real depth/apparent depth
Related to wave velocities
n = cm/cv
Serial relation
n1sin1 = n2sin2
Thin prism
d = (n – 1)A
Critical angle(c)
n = 1/sin c
Lens formulae
1/u + 1/v = 1/f
Telescope magnification
m = fo/fe
Angular magnification
M = - (D/f+ 1)
Resolving power
 = I .22/a
Physical Optics
Constructive interference
path difference = m
Destructive interference
path difference = (2m + 1)/2
Young’s slits
m = xmd/D
Newton’s rings (dark ring viewed by reflection)
m = rm2/R
Thin film interference
m = 2nt cos r
Diffraction grating (max)
m = e sin 
Brewster’s law (polarisation)
tan p = n
Malus’ law
I = Io cos2 
Doppler effect
 = v/c f = fv/c
Travelling wave
y = a sin[t – kx]
Travelling wave
y = a sin2[t/T – x/]
1
Standing wave
y = 2a cos[2x/]sin[2t/T]
Velocity of sound
v = [P/r]1/2
Frequency of stretched string fo = 1/2L[T/m]1/2
Fundamental frequency (closed tube) f o = v/4L
Intensity of wave
I = ka2
Beat frequency
f = f1 – f2
Organ pipes:
Open pipe
f = (m + 1)fo
Closed at one end
f = (2m + 1)fo
Thermal Physics
Scale of temperature t/100 = (Ft – Fo)/(F100 – Fo)
Linear expansivity (a)
l = lo[1 + ]
Specific heat capacity (c)
H = mc
Specific latent heat (L)
H = mL
Electrical heating
H = VIt
Density change
 = o[1+]
Ideal gas equation
PV = nRT
Isothermal change
PV = constant
Adiabatic change
PV = constant
Charles’s law
V/T = constant
Conduction of heat
dH/dt = - kA d/dx
Stefan’s law
E = A[T4 – To4]
Wien’s law
max = constant
First law of thermodynamics
dU = dQ + dW
Work done in isothermal change dW = PdV
Kinetic theory equation
PV = ⅓ mnc2rms
Mean square velocity
crms = √[u12 + u22 + …. +un2]/n
Electricity
Charge
Q = It
Current
I = nAve
Electrical energy
Energy = QV
Force on charge
F = QE = QV/d
Ohm’s law
V = IR
Internal resistance
E = I[R + r]
Resistivity
= RL/A
Temperature variation
R = Ro[1 + ]
Series resistance
R = R1 + R 2
Parallel resistance
1/R = 1/R1 + 1/R2
Power
W = VI = I2R = V2/R
Electric field strength
E = - dV/dx
Force between point charges F = Q1Q2/[4d2]
Field due to point charge Q
E = Q/[4d2]
Potential
V = W/Q0
Potential due to charge Q
VE = Q/[4d]
Capacitance
C = Q/V
Capacitance of a sphere
C = 4r
Parallel-plate capacitor
C = A/d
Parallel capacitors
C = C1 + C 2
Series capacitors
1/C = 1/C1 + 1/C2
Energy stored
E = ½ CV2 = ½ QV = ½ Q2/C
Capacitor discharge
V = Voe-t/RC
Capacitor charge
V = Vo [1 -e-t/RC]
Electromagnetism
Force on current
Couple on coil
Field at centre of coil
Field in solenoid
Field at end of long solenoid
Helmholtz coils
Field near straight wire
Velocity of e.m. waves
Electromagnetic induction
Self-inductance
Mutual inductance
Induced e.m.f. ()
Induced e.m.f. (s)
Induced e.m.f. in a rotating coil
Induced e.m.f.
(Neumann’s law)
Transformer
F = BIL
C = BANIsin 
B =oNI/2r
B = oNI/L
B = 8oNI/5√5r
B =oI/2r
c = 1/(oo)1/2
L = N/I
M = Nss/Ip
 = -L dI/dt
s = - MdI/dt
 = BAN sin
 = - Nd/dt
np/ns = Vp/Vs
Ip/Is = ns/np
I = io/√2
i = io sin(t)
Xc = 1/C
XL = L
Root mean square current (I)
Alternating current
Capacitative reactance
Inductive reactance
Impedance (series RLC)
Z = [R2 + (XL - XC)2]1/2
Resonance condition for 
XL = XC
Electron Physics
Electrostatic force on electron F = eE
Electromagnetic force on electron F = Bev
Crossed fields
eE = Bev
Energy gain
E = eV
Kinetic energy
eV = ½ mv2
Circular orbit
Bev = mv2/r
Quantum energy
E = hf
Relativistic mass-energy relation E = mc2
de Brogue equation
 = h/p = h/mv
Work function
W = hfo
Einstein’s p.e. equation
hf = hfo + ½ mv2
Photoelectric effect
hf = eV
Nuclear Physics
Radioactive decay
N = No e-t
A = Ao/2n
Half-life
T = ln2/
Serial relation
1N1 = 2N2
Nuclear radius
r = roA1/3
2