Physics 201
•
Exam Information Sheet
ĉ = c/c or c = c = c ĉ
a = ∆v/∆t → a is the slope of velocity
A · B = |A||B| cos θ
v = ∆x/∆t → v is the slope of position
ΣF = m a
g = 9.8 m/s2
RE = 6.4 × 106 m
G = 6.67 × 10−11 N·m2 /kg2
v(t) = vo + a t
x(t) = xo + vo t + 12 a t2
vf 2 = vo 2 + 2 a (xf − xo )
vave = 12 (vf + vo )
N force is perpendicular to surfaces
W = mg
tan θ = opp / adj
sin θ = opp / hyp
cos θ = adj / hyp
Fr = −m v 2 r̂/R
a = −r ω 2 r̂ + r α θ̂
arad = − v 2 r̂/R
atan = ∆|v|/∆t
vC/A = vC/B + vB/A
Ffric ≤ µ N,
Vsphere =
Asphere = 4πR2
4
3
πR3
N = normal
Acircle = πR2
Ccircle = 2πR
√
−b ± b2 − 4ac
2
a x + b x + c = 0 then x =
2a
W = F · x = |F||x| cos θ
(work)
K=
1
2
2
mvcm
W = ∆K
∆K = Kf − Ki = 12 m(vf2 − vi2 )
U = − F · x (potential energy)
Fx = −∆U/∆x
F = kx
Fm = −GM m r̂/r 2
(linear spring)
Usurface = mgh
U = −GM m/r
∆U + ∆K + ∆Q = 0
m1 v1 + m2 v2 = (m1 + m2 )vf
v1f = v1i (m1 − m2 )/(m1 + m2 )
v2f = v1i (2 m1 )/(m1 + m2 )
F = ∆p/∆t
∆p = pf − pi = mvf − mvi
J ≡ F ∆t = ∆p
|∆Q| = Ffric d
vf = vi + vexh ln(mi /mf )
xcm = ( mi xi )/M, M =
mi
U = 12 k x2
P = F · v = ∆E/∆t
(linear spring)
(power)
θ = θo + ωo t + 12 αt2
ω = ∆θ/∆t = ωo + αt
ω 2 = ωo2 + 2 α (θ − θo )
α = ∆ω/∆t
s = rθ
v = rω
a = rα
Krot = 12 Iω 2
2
I=
r ∆m
2
Ktotal = 12 mvcm
+ 12 Iω 2
Ipt mass = mr 2
Isolid sphr = 25 mr 2
Isolid cyl = 12 mr 2
Isphr shel = 23 mr 2
Ihoop = mr 2
Irod, center =
1
m2
12
Irod, end = 13 m2
Σ τ = I α
,
τ = r⊥ F
I = Icm + m h2
L = m r × v = r × p = I
ω
τ = ∆L/∆t
τ ∆t = ∆L
ω = 2πf = 2π/T
T = 2π I/κ (torsion pendulum)
Li = Lf
ω = k/m (spring-mass oscillator)
T = 2π I/(m g xcm ) (simple pendulum)
x(t) = xmax cos(ωt + φ)
v(t) = −xmax ω sin(ωt + φ)
a(t) = −xmax ω 2 cos(ωt + φ)
x(t) = xmax cos(ω t + φ)e−bt/(2m)
a(t) + ω 2 x(t) = 0
ω = k/m − b2 /(4m2 )
Etotal (t) = 12 kx2max e−bt/m
xCG = ( gi mi xi )/( gi mi )
resonance: ωdriven = ω
xCG = xcm = ( mi xi )/M
F = Y A ∆L/Lo
vesc = 2GM/R
p = F/A
RSchw = 2GM/c2
c = 3.0 × 108 m/s
Etotal = −GM m/(2r)
∆A/∆t = constant
4π 2 r 3 = GM T 2
ρ = m/V
p = po + ρgh
Fbuoy = ρfld g Vdsplcd
Wapp = W − Fbuoy
ρ1 A1 v1 = ρ2 A2 v2 = dm/dt
p1 + ρgy1 + 12 ρ v12 = p2 + ρgy2 + 12 ρ v22
y(x, t) = ymax sin(kx − ωt)
k = 2π/λ
v = ω/k = λ/T = λf
v = F/µ , µ = m/
sin x + sin y = 2 sin[(x + y)/2] cos[(x − y)/2]
fn = nv/(2L),
gi =constant
n = 1, 2, . . .
2
Pave = 12 µv ω 2 ymax
solids: v =
Y /ρ
nodes: x = nλ/2
fluids: v =
n = 1, 2, . . .
B/ρ
vsound/air = 343 m/s
I = Psource /(4πr 2 )
β = 10 log10 (I/Io ) dB
Io = 1 × 10−12 W/m2
f = f (v ± vlistener )/(v ± vsource ), numerator: + listener moving TOWARD source
numerator: − listener moving AWAY from source
denominator: + source moving AWAY from listener
denominator: − source moving TOWARD listener
TF = 95 TC + 32
TK = TC + 273.15
∆L = αLo ∆T
∆V = 3 αVo ∆T
Q = cm∆T
Qcond = kAt∆T /L
Qrad = σtAT 4
Prad = Qrad /t
σ = 5.67 × 10−8 W/(m2 ·K4 )
Blackbody: = 1
P V = kN T
k = 1.38 × 10−23 J/K
N = nNA
NA = 6.022 × 1023 particles/mol
R = NA k = 8.31 J/(mol·K)
P V = RnT
N k = nR
Qlat = mL
M = mNA
√
vrms = v 2 = 3k T /m = 3R T /M
K = 12 mv 2 = 32 kT
U = N K = 32 N kT = 32 nRT
∆W = P ∆V , P = pressure
∆Q − ∆W = ∆U
Wiso
thrm
= nRT n(Vf /Vi )
adiabatic: ∆Q = 0
Qv = nCv ∆T
Qp = nCp ∆T
monatomic: Cv = 32 R
monatomic: Cp = 52 R
all ideal gases: Cp − Cv = R
γ = Cp /Cv
adiabatic: P1 V1γ = P2 V2γ
= W/Qh = (Qh − Qc )/Qh
carnot = 1 − (Tc /Th )
COP = Qc /W
∆S = Q/T
∆Suniverse ≥ 0