Page 556 - Physics Coursebook 2015 (A level)

Cambridge International AS and A Level Physics
544
Mathematical equations
arc length = rθ
circumference of circle = 2πr
area of circle = πr2
curved surface area of cylinder = 2πrh volume of cylinder = πr2h
surface area of a sphere = 4πr2
volume of sphere = 43 πr3
Pythagoras’ theorem: a2 = b2 + c2 cosinerule:a2 =b2+c2−2bccosA
abc sine rule: sin A = sin B = sin C
for small angle θ: sinθ ≈ tanθ ≈ θ and cosθ ≈ 1 lg(AB) = lg(A) + lg(B)
Formulae and relationships
uniformly accelerated motion
work done on or by a gas
gravitational potential hydrostatic pressure
pressure of an ideal gas
simple harmonic motion velocity of a particle in s.h.m.
Doppler effect electric potential
capacitors in series
capacitors in parallel
energy of charged capacitor
electric current resistors in series
resistors in parallel
Hall voltage
alternating current or voltage radioactive decay
decay constant
v = u + at
s = 12 ( u + v ) t s = ut+12at2 v2 =u2+2as W = pΔV
φ = –Gm r
p = ρgh
p = 13 N m < c 2 >
lg AB = lg(A) − lg(B) n
v = v0cosωt
v = ± ω ( x 20 − x 2 )
f0= fsv v±vs
V=Q 4πε0r
C1 = C1 + C1 + ... 12
C = C1 + C2 + ... W = 12 Q V
I = nAvq
R = R1 + R2 + ...
R1 = R1 + R1 + ... 12
VH = BI ntq
x = x0sinωt
x = x0exp(−λt) or
x = x0e−λt
λ = 0.693
t 12
ln(x ) = nln(x) ln(ekx) = kx
V a = −ω2x