Harold S AP Physics

Mechanics: Linear / Mechanics: Angular / Electricity / Magnetism / Fluid Mechanics / Thermo-dynamics / Atomic and Nuclear /
Waves and Optics

Harold’s AP Physics

“Cheat Sheet”

23 February 2016

Mechanics:
Linear Translation / Mechanics:
Angular / Rotational Motion / Electricity / Magnetism / Fluid Mechanics / Thermo-dynamics / Atomic and Nuclear /
Waves and Optics
Kinematics
Position
(m)
(rad) / Horizontal:
x= x0+vx0t+12at2
Vertical:
y= y0+vy0t-12gt2
x= x0+vt
s=rθ
x=vdt / θ=θ0+ω0t+12αt2
x=Acosωt
x=Acos2πft / 10-24=yocto
10-21=zepto
10-18=atto
10-15=femto
10-12=pico
10-9=nano
10-6=micro
10-3=milli
100=1
103=kilo
106=mega
109=giga
1012=tera
1015=peta
1018=exa
1021=zetta
1024=yotta / Fluid Mechanics:
P1+ρgy1+12ρv12=P2+ρgy2+12ρv22
(Conservation of Mass)
ρ=mV
∆l=αl0∆T / Waves and Optics:
1si+1so=1f
∆L=mλ
dsinθ=mλ
Relativity:
L=L01-v2c2
Velocity
(m/s)
(rad/s) / v=dt=∆x∆t=dxdt
v= v0+at
v2=v02+2a(x-x0)
v=v0+v2
v=rω
v=ω×r
v=adt / ω=θt=∆θ∆t=dθdt
ω=ω0+αt
ω2=ω02+2α(θ-θ0)
ω=ω0+ω2
ω=2πT=2πf
ω=km=gl / Speed of Light:
c≈3.00 x 108 ms
=299,792,458 ms / Fluid Mechanics:
A1v1=A2v2
vrms=3RTM
vrms=3kBTμ / Waves and Optics:
v=fλ
n=cv
n1sinθ1=n2sinθ2
Relativity:
v(t)= v01-v2c2
Acceleration
(m/s2)
(rad/s2) / a=vt=∆v∆t=dvdt
a=Fm=Fnetm
a=rα
g=9.80665 ms2
g=32.1740 fts2 / Tangential:
α= aTr=∆ω∆t=dωdt
α=τI=τnetI
Centripetal:
ac= v2r=ω2r
a2=ac2+aT2 / NA / NA / NA
Jerk (Jolt)
(m/s3)
(rad/s3) / j=at=∆a∆t=dadt / ζ=αt=∆α∆t=dαdt / NA / NA / NA
Dynamics
Mass
(kg)
/
Moment of Inertia
(kg•m2) / m = actual mass
I = effective mass / I=mr2
I=r2dm
I=r•dm / me=9.11 ×10-31 kg
mp≈mn=1.67 ×10-27 kg / NA / Relativity:
m=m01-v2c2
Momentum
(kg•m/s)
(kg•m2/s) / p=mv
∆p=m∆v
Conservation of Momentum:
pi=pf / L=Iω
L=r×p
L=r×v dm / NA / Fluid Mechanics:
∇p=ρg / Atomic and Nuclear:
λ=hp
Relativity:
p=mv1-v2c2
Force
(N = kg•m/s2)
/
Torque
(J = N•m) / F=ma
Fg=mg
F=Fnet=ma
F=pt=∆p∆t=dpdt
Ffric≤μN
Fs=-kx
FG=-Gm1m2r2
FG=-Gm1m2r2 r / τ=rFsinθ
τ=τnet=Iα
τ=rF=Iα
τ=r×F
τ=dLdt
F=mac
F=mv2r
F=mrω2 / Electricity:
F=kq1q2r2
F=14πϵ0 q1q2r2
F=Eq
Magnetism:
FB=qvBsinθ
FB=BIlsinθ
FB=qv×B
FB=Il×B
F=I dl×B / Fluid Mechanics:
F=PA
P=FA=ρhg
Fbuoy=ρVg
PV=nRT=NkBT
R=8.31Jmol•K
kB=1.38 ×10-23 JK / NA
Impulse
(N•s)
(N•m•s) / J=F ∆t=∆p=m ∆v
J=F dt=∆p / H=τ ∆t=∆L=I ∆ω
H=τ dt=∆L / NA / NA / NA
Yank
(N/s2)
/
Rotatum
(J/s) / Y=m J
Y=Ft=∆F∆t=dFdt / P=r×Y
P=τt=∆τ∆t=dτdt / NA / NA / NA
Energy
Work
(J = N•m) / W=Fd
W=F ∆xcosθ
W=F•dr / W=τ ∆θ
W=τ (θ-θ0)
W=τ•dθ / W=QV / Thermodynamics:
W=-P ∆V
e=WQH
ec=TH-TCTH / NA
Kinetic
Energy
(J) / K=12mv2 / K=12Iω2 / 1 eV=1.60 ×10-19 J / Fluid Mechanics:
P+ρgy+12ρv2=constant
Thermodynamics:
Kavg=32kBT / Atomic and Nuclear:
Kmax=hf-ϕ
Relativity:
K=
m0c2 11-v2c2-1
Potential
Energy
(J) / ∆Ug=mgh
UG=-Gm1m2r
G=6.67 ×10-11 / Coiled spring:
Us=-12kx2 / UE=qV
UE=14πϵ0 q1q2r
Uc=12QV
Uc=12CV2
UL=12LI2 / Fluid Mechanics:
P=P0+ρgh
Thermodynamics:
∆U=Q+W / Atomic and Nuclear:
E=hf=pc
E=mc2
∆E=(∆m)c2
Relativity:
E=mc2 11-v2c2
Heat
Energy
(J) / Conservation of Energy:
Ei=Ef
E=W+Q+K+∆Ug+UG+Us+UE+Uc+UL+…=constant / NA / NA / Thermodynamics:
H=kA∆TL
Q=mHf
Q=mHv
∆E=Q=mC∆T
mC∆T=mCTf-Ti
CH2O=4180 J/Kg °K
Tf=m1C1∆T1i+m2C2∆T2im1C1+m2C2 / NA
Power
(W) / P=W∆t=Fv
P=∆E∆t=dEdt
P=Fvcosθ
P=F•v / P=W∆t=τω
P=∆W∆t=dWdt
P=τωcosθ
P=τ•ω / P=IV
P=I2R
P=V2R / NA / NA
Engineering Application
Period / Frequency
(Hz) / T=1f
f=1T / T=1f=2πω
Ts=2πmk
Tp=2πlg / T=2πb
For:
y=sinbθ
y=cosbθ / NA / Waves and Optics:
f=λv
Relativity:
t= t01-v2c2
Center
of Mass
(m) / xCM=m1x1+m2x2m1+m2
xCM=miximi
x=1M 0Mx dm
where M=0Mdm
and dm=ρ dz dy dx / rCM=mrm / NA / NA / Waves and Optics:
M=hiho=siso
(magnification)
Rigid Bodies / Fy=mg=0
(Down = ‘−‘) / τ=FyxCM=0
(CW = ‘−‘) / NA / NA / NA

Mechanics: Linear / Mechanics: Angular / Electricity / Magnetism / Fluid Mechanics / Thermo-dynamics / Atomic and Nuclear /
Waves and Optics

Mechanics: Linear / Mechanics: Angular / Electricity / Magnetism / Fluid Mechanics / Thermo-dynamics / Atomic and Nuclear /
Waves and Optics
Electricity
Electricity
Electric
Field
(V/m)
(N/C) / E=Fq
Eavg=-Vd
E=-dVdr
Gauss’s Law:
E•dA=Qϵ0
E=ρJ / Capacitance
(F) / C=QV
C=ϵ0Ad
C =κϵ0Ad
Cp= iCi
1Cs= i1Ci
Potential
(V) / V=IR
V=QC
V=kiqiri
V=14πϵ0iqiri / Resistance
(Ω) / R=VI
R=ρlA
Rs= iRi
1Rp= i1Ri
Current
(A) / Iavg=∆Q∆t
I=dQdt
I=VR
I=NevdA
e=1.60 ×10-19 C / EMF
(V) / Faraday’s Law of Induction:
E•dl=- ∆ϕm∆t
ε=-LdIdt

Mechanics: Linear / Mechanics: Angular / Electricity / Magnetism / Fluid Mechanics / Thermo-dynamics / Atomic and Nuclear /
Waves and Optics

Mechanics: Linear / Mechanics: Angular / Electricity / Magnetism / Fluid Mechanics / Thermo-dynamics / Atomic and Nuclear /
Waves and Optics
Magnetism
Magnetism
Magnetic
Field
(T) / B=μ02π Ir
Solenoid:
Bs=μ0nI
where n=Nl turns per meter
Ampere’s Circuit Law:
B•dl= μoI
dB=μ04π I dl×rr3
μ0=4π ×10-7(T•m)A
Magnetic
Flux
(Wb) / ϕm=BAcosθ
Gauss’s Law for Magnetism:
ϕm=B•dA
EMF
(V) / εavg= - ∆ϕm∆t
ε=Blv

Mechanics: Linear / Mechanics: Angular / Electricity / Magnetism / Fluid Mechanics / Thermo-dynamics / Atomic and Nuclear /
Waves and Optics