Motions in a circle
Syllabus
● w = 2π / T [w is angular
velocity]
● v = rw = 2πfr
● a = rw2
● a = v2 / r
● F = mrw2
● F = mv2 / r
Gravitational Fields
Syllabus
●
●
●
●
F = Gm1m2 / r2
*g = GM / r2
Φ = -GM / r
*Ep = -GMm / r
Non-syllabus
● v2 = GM / r
● T2 = (4π2 / GM) r3
● ΔΦ = GM (1/r1 - 1/r2)
Temperature
Syllabus
● T/K = θ/oC + 273.15
● E = mcΔθ
● E = mL
Ideal Gases
Syllabus
● pV = nRT
●
●
●
●
pV = NkT ; k = R / NA
*pV = ⅓ Nm<c2>
cr.m.s. = √<c2>
*EK = 3/2 kT
Thermodynamics
Syllabus
● W = pΔV
● ΔU = q + W [U is internal
energy; q is energy supplied by
heating; W is work done on the
system]
Oscillations
Syllabus
a = -w2x
x = xo sin wt [solution to previous]
v = vo cos wt
v = ±w √(xo2 - x2) [when v = max;
x = 0]
● E = ½ mw2xo2
●
●
●
●
Electric Fields
Syllabus
● F = qE
● E = ΔV / Δd
● F = Q1Q2 / (4πε0r2)
● E = Q / (4πε0r2)
● V = Q / (4πε0r)
● Ep = Qq / (4πε0r) = Q1Q2 /
(4πε0r)
Non-syllabus
● E = -V / d
● F = eV / d for an electron with
charge -e
● F = -QV / d
● V = W / Q
● ΔV = Q / 4πε0 [1/r1 - 1/r2]
Capacitance
Syllabus
●
●
●
●
●
●
●
C=Q/V
W = ½ QV = ½ CV2
τ = RC
x = xoe-t / RC
Parallel: Ctotal = C1 + C2 + C3 + …
Series: 1 / Ctotal = 1/C1 + 1/C2 + …
Capacitance of a sphere C = 4πε0r
● V = Q / 4πε0r
Magnetic Fields
Syllabus
●
●
●
●
F = BIL sin θ
F = BQv sin θ
*VH = BI / (ntq) [t = thickness]
Φ = BA cos θ
Non-syllabus
●
●
●
●
r = mv / Be → p = Ber
e / me = v / Br
e / me = (2Vca) / (r2B2)
E = - Δ(NΦ) / Δt
Alternating Currents
Syllabus
● x = x0 sin ωt
● Ir.m.s. = I0 / √2
● Vr.m.s. = V0 / √2
Quantum Physics
Syllabus
● E = hf [h is planck constant; f is
frequency]
● p = E / c [p is momentum; c is
speed of light]
● hf = Φ + ½ mv2 max
● λ = h / p = h / mv
● hf = E1 - E2
Non-syllabus
● E = hc / λ
●
●
●
●
eV = ½ mv2 → v = √[(2eV) / m]
f=E/h
λ=c/f
[for electron diffraction]: λ = 2d sin
θ
Nuclear Physics
Syllabus
● E = mc2 ; E = c2Δm
● A = λN
● λ = 0.693 / t1/2
● x = x0e-λt [ x can represent A, N or
R - quantity left at time t]
● λ = ln(2) / t1/2 = 0.693 / t1/2
Medical Physics
Syllabus
● Z = ρc [Z = specific acoustic
impedance; c = speed of sound in
material]
● α = Ir / I0 = (Z2 - Z1)2 / (Z2 + Z1)2
● I = Ioe-µx
Non-syllabus
● Emax = eV
1. fmax = eV / h
2. λmin = hc / eV
● Thickness of bone = cΔt / 2 [c =
speed of sound in bone]
Astronomy and
Cosmology
Syllabus
● F = L /(4πd2) [F is radiant flux
intensity]
● λmax ∝ 1 / T → λmaxT = 2.9 x 10-3
mK
● L = 4πσr2T4
● ∆λ / λ ≈ ∆f/f ≈ v / c
● v ≈ H0d
Non-syllabus
● T0 = 1 / H0
0
