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GREAT Phys Mech Rot Grav Waves Fluids Thermo EandM EMRad Optics

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General Physics Equation Summary Sheet
SI UNITS
KINEMATICS
Length
Mass
Time
Electric current
Temperature
Luminous intensity
Δx
∆x
v=
∆t
∆v
a=
∆t
No
Acceleration
Δx = vt
m
kg
s
A
K
Cd
DERIVED UNITS
m3
N
J
W
Pa
C

F
Volume
Force
Energy/Work
Power
Pressure
Charge
Resistance
Capacitance
MECHANICS
Displacement
Velocity
Acceleration
Uniform
Acceleration
Δx = vavgt
Δx = vit + ½at2
Fg = G
vf2 = vi2 + 2aΔx
vf = vi + at
MOMENTUM AND COLLISIONS
p = mv
FΔt = Δp
momentum
Impulse-Momentum Theorem
Elastic Collisions
Perfectly Inelastic Collisions
pi = p f
KEi = KEf
pi = p f
KEi > KEf
Linear
Angular
Relation
Δx
∆x
v=
∆t
∆v
a=
∆t
Δθ
∆θ
ω=
∆t
∆ω
α=
∆t
Δx = r Δθ
v = rω
a = r
No Acceleration
Uniform Acceleration
linear angular linear
angular
Δx = vt
Δθ = ωt
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N ∙ m2
kg 2
Gravitational Constant
W = mg
Weight
Ffmax = μs FN
Static Friction
Ff = μk FN
Kinetic Friction
Δx = vavgt
Δx = vit + ½at2
vf2 = vi2 + 2aΔx
vf = vi + at
W = (Fcosθ)d
E = KE + U
KEi + Ui = KEf + Uf
KE = ½mv2
Work
Mechanical Energy
Conservation of Mechanical Energy
Kinetic Energy (Translational)
Ugravitational = mgy
Uelastic = ½kx2
WNC = ΔE
Wnet = ΔKE
F = -kx
W
P=
= Fv
∆t
Gravitational Potential Energy
Elastic Potential Energy
Work of Nonconservative Forces
Work-Energy Theorem
Hooke’s Law (Spring Force)
Power
UNIFORM CIRCULAR
MOTION
v2
ac =
r
mv 2
F = ma c =
r
ROTATIONAL KINEMATICS
Acceleration
Gravity
WORK AND ENERGY
1012
109
106
103
10-2
10-3
10-6
10-9
10-12
10-15
10-18
Displacement
Velocity
m1 m2
r2
G = 6.67 × 10−11
METRIC PREFIXES
Terra
Giga
Mega
kilo
centi
milli
icro
nano
pico
femto
atto
Newton’s Laws of Motion
If F = 0, then v = constant
F = ma
F1→2 = -F2→1
1st Law
2nd Law
3rd Law
Δθ = ωavgt
Δθ = ωit + ½t2
ωf2 = ωi2 + 2Δθ
ωf = ωi + t
Centripetal
Acceleration
Centripetal
Force
ROTATIONAL DYNAMICS
 = F⊥ r
 = (Fsinθ) r
I = ∑mr2
xCG =
∑ mi xi
∑ mi
∑F = 0
∑τ = 0
Torque
Moment of
Inertia
Center of
Gravity
Conditions for
Equilibrium
Angular
Linear
Δθ
ω
α
I
τ
τ = I α
KErot = ½I2
W = τ(Δθ)
L = I
d
v
a
m
F
F = ma
KE = ½mv2
W = Fd
p = mv
1
ELASTICITY OF SOLIDS
F
∆L
=Y
A
L0
F
∆x
=S
A
h
∆P = −B
∆V
V
Stretching/Compression
Shear Deformation
S. G. =
Volume Deformation
P = fluid g h
GASES
F
P=
A
p1V1 = p2V2
V1 V2
=
T1 T2
V1 V2
=
n1 n2
p1 V1 p2 V2
=
T1
T2
Pressure
Boyle’s Law
Charles’ Law
Avogadro’s Principle
Combined Gas Law
pV = nRT
ptotal = pA + pB + pC + …
pA = χA ptotal
FLUIDS
m
ρ=
V
Perfect Gas Law
Dalton’s Law of Partial Pressures
SIMPLE HARMONIC MOTION
Density
ρ
P = P0 + fluid g h
FB = Wfluid displaced
FB=(fluid)(Vsubmerged)(g)
ρobject
% submerged =
× 100
ρfluid
F1 F2
=
A1 A 2
A1d1 = A2d2
F = Av
A1v1 = A2v2
P1 + ½v12 + gy1 = P2 + ½v22 + gy2
q
C=
∆T
C
Cs =
m
C
Cm =
n
δU
∆U
CV = ( ) =
δT V ∆T
δH
∆H
CP = ( ) =
δT P ∆T
U = q + w
x = Acos(ωt)
Displacement
v = -Aωsin(ωt)
vmax = Aω
a = -Aω2cos(ωt)
amax = Aω2
1
f=
T
2π
ω = 2πf =
T
Velocity
k
ω=√
𝑚
Frequency Factor
for Springs
g
L
x = Acos(ωt + ϕ)
Frequency Factor
for Pendulums
ϕ = phase shift
H = U + pV
y(x,t) = Acos(ωt ± kx)
ω = 2f
2π
k=

1st Law
Acceleration
Frequency / Period
Frequency Factor
ω=√
Standing Waves
f = v
2L
n
4L
n =
n
n =
Wave Speed
n = 1,2,3. ..
n = 1,3,5. ..
T
v=√
μ
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String fixed at both ends
Pipe open at both ends
String fixed at one end
Pipe open at one end
Wave Velocity on a String
Specific Gravity
ρ𝐻2𝑂
Hydrostatic Pressure
(Gauge Pressure)
Absolute Pressure
Buoyancy Force
Pascal’s Principle
(Hydraulic Jack)
Hydraulic Jack
Flow Rate
Continuity Equation
Bernoulli’s Equation
THERMODYNAMICS
Heat Capacity
Specific Heat Capacity
Molar Heat Capacity
Constant Volume Heat Capacity
Constant Pressure Heat Capacity
Change in Internal Energy
q = ∫ CV dT
Constant V
w = ∫ −pext dV
Universal
q = ∫ CP dT
Constant P
w = −p∆V
Constant pext
q = −w
Constant T
w = −nRTln
H = qp
CP – CV = nR
Laws of Thermodynamics
nd
2 Law
Vf
Vi
Reversible,
Isothermal
Enthalpy
Enthalpy Change at Constant p
For a Perfect Gas
Energy can’t be created or destroyed.
For a spontaneous process, ΔSuniverse > 0.
rd
3 Law
A perfectly ordered crystal at 0K has zero entropy.
qrev
Entropy Change
∆S =
T
Vf
pi
Entropy Change during
∆S = nRln = nRln
Expansion/Compression
Vi
pf
Tf
Entropy Change during heating
∆S = nC ln
Ti
2
SOUND
v = f
Y
v=√
ρ
P
v=√
ρ
v = 331m/s√
T
273K
P
P
=
A 4πr 2
I
β = 10log
𝐼0
I=
W
𝑚2
v ± 𝑣0
𝑓0 = 𝑓𝑠
v ∓ 𝑣𝑠
DC CIRCUITS
Speed of Sound
Speed of Sound in a Metal Rod
q
C=
∆v
Speed of Sound in a Gas
Q(t) = Q max (1 − e−τ )
Temperature Dependence on
the Speed of Sound
Capacitance
Capacitor Charging
t
t
V(t) = ε (1 − e−τ )
Intensity of Sound
Intensity Level
I(t) =
ε −t
e τ
𝑅
Capacitor Discharging
𝐼0 = 10−12
Doppler Effect
ELECTRIC FIELDS AND FORCES
e = 1.602×10-19C
𝑞1 𝑞2
F = |𝑘 2 |
𝑟
F = qE
𝑞
E = |𝑘 2 |
𝑟
Q
𝐸 = EAcosθ =
ϵo
q
V=k
r
U = qV
ΔV = -Ed
W = qΔV
W = -qΔV
t
Q(t) = Q max e−τ
t
V(t) = ε e−τ
Fundamental charge
Coulomb’s Law
Force due to an Electric Field
Electric Field due to a Point
Charge
Gauss’s Law
(Electric Flux)
Potential due to a Point Charge
Potential Energy of a Point
Charge
Relationship between ΔV and E
Work done against an electric
field
Work done by an electric field
I(t) =
ε −t
e τ
𝑅
C = ε0
A
d
A
C =  (ε0 )
d
1
1
Ustored = C∆V 2 = Q∆V
2
2
1
1
1
= + +. ..
Ceq C1 C2
Ceq = C1 + C2 +. ..
∆q
I=
∆t
ΔV = IR
L
R=ρ
A
 = 0(1 + ΔT)
R = R0(1 + ΔT)
P = ∆VI = I 2 R =
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Parallel Plate Capacitor
∆V 2
R
Potential Energy Stored by a
Capacitor
Capacitors in Series
Capacitors in Parallel
Current
Ohm’s Law
Resistance of a Wire
Temperature Dependence of the
Resistivity and Resistance
Power Dissipated by a Resistor
R eq = R + R 2 +. ..
1
1
1
= + +. ..
R eq R R 2
Current entering a junction =
Current exiting a junction
Resistors in Series
Resistors in Parallel
The potential difference around
any closed loop sums to zero.
Kirchoff’s Loop Rule
Kirchoff’s Junction Rule
3
MAGNETIC FIELDS AND FORCES
F = qvBsinθ
Magnetic Force on a
Charged Particle in
Motion
Magnetic Force on a
Current-carrying Wire
F = BI  sinθ
INDUCED VOLTAGES AND INDUCTANCE
B = B⊥A = BAcosθ
∆B
ε = −N
∆t
ΔV = B  v⊥
ε = NBAω sinωt
∆B21
∆I
ε1 = −N1
= −M
∆t
∆t
Magnetic Flux
Faraday’s Law
(Induce Emf)
Motional Emf
Generator Emf
Mutual Inductance
∆B12
∆I
= −M
∆t
∆t
∆B
∆I
ε = −N
= −L
∆t
∆t
ε2 = −N2
τ = BIANsinθ
B=
Torque on a CurrentCarrying Loop
Magnetic Field Due to
a Current Carrying
Wire
μ0 I
2πr
μ0 I
B=N
2R
B=
Magnetic Field at the
Center of a Circular
Current-Carrying Loop
μ0 NI
= μ0 nI
L
∆B
∆B
=N
∆I
I
ΔV1I1 = ΔV2I2
∆𝑉1 𝑁1 𝐼2
=
=
∆𝑉2 𝑁2 𝐼1
∆I
ε = −L
∆t
L=N
I(t) =
AC Potential
Rms Potential
Rms Current
Power Dissipated in a Resistor
Ohm’s Law
Capacitive Reactance
ΔVC,rms = Irms XC
XC = 2πfL
Inductive Reactance
ΔVL,rms = Irms XL
+ (XL − XC
ΔVmax = Imax Z
ΔVrms = Irms Z
1
f0 =
2π√LC
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Emf in an RL Circuit
τ=
PEL = ½ LI2
AC (ALTERNATING CURRENT) CIRCUITS
Z=
t
ε
(1 − e−τ )
R
Transformers
L
R
Current in an RL
Circuit
Potential Energy
Stored in an Inductor
Magnetic Field Inside
an Ideal Solenoid
ΔV = ΔVmax sinωt
∆Vmax
∆Vrms =
√2
∆𝐼𝑚𝑎𝑥
∆I𝑟𝑚𝑠 =
√2
P = Irms2 R
ΔVmax = Imax R
ΔVrms = Irms R
1
1
XC =
=
2πfC ωC
√R2
Self-Inductance
)2
Impedance of RLC Circuits
Resonance Frequency in LC Circuits
c=
1
ELECTROMAGNETIC RADIATION
√ε0 μ0
= 3.0 × 108 m
c
n=
v
λf = v
Ephoton = hf
1
uE = ε0 E 2
2
1 2
uB =
B
2μ0
P
I=
A
u
fO = fS (1 ± )
c
1
I = I0
2
I = I0 cos 2 θ
Speed of Light in a Vacuum
/s
Index of Refraction
Wavelength/Frequency of
Light
Energy of a Photon
Energy density of the
Electric Field
Energy density of the
Magnetic Field
Intensity of Light
Doppler Effect
Unpolarized light
transmitted through a
polarizing filter
Polarized light transmitted
through a polarizing filter
4
REFLECTION AND REFRACTION
θincidence = θreflection
n1 sinθ1 = n2 sinθ2
c
n=
v
𝑛2
sinθ𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 =
𝑛1
𝑛2
d′ = 𝑑
𝑛1
Law of Reflection
Snell’s Law of Refraction
Index of Refraction
Critical Angle for Total Internal
Reflection
Apparent depth
MIRRORS AND LENSES
f=½R
1 1 1
+ =
𝑝 𝑞 𝑓
ℎ𝑖
𝑞
m=
=−
ℎ𝑜
𝑝
Focal Length
Thin Mirror and
Lens Equation
Magnification
𝐿𝑒𝑛𝑠 𝑃𝑜𝑤𝑒𝑟 =
f number =
𝑓
𝐷
1
𝑓𝑚
a sinθdark = m
Dark Fringes (Double Slit Interference)
Thin Film Interference
Destructive Interference (No Phase Shift)
Thin Film Interference
Destructive Interference (Phase Shift)
Bright Fringes (Diffreaction Grating)
Dark Fringes (Single Slit Interference)
CONSTANTS
2
9.80 m/s
F number
G
6.67×10-11 N∙m2/kg2
Gravitational acceleration near the
surface of the Earth
Gravitational constant
ME
RE
R
ke
0
e
5.98×1024 kg
6.38×106 m
8.314 J/mol∙K
8.99×109 N∙m2/C2
8.85×10-11 C2/N∙m2
1.62×10-31 C
Mass of the Earth
Radius of the Earth
Universal gas constant
Coulomb constant
Permitivity of Free Space
Fundamental charge
me
mp
9.11×10-31 kg
1.67×10-27 kg
0
c
4×10-7 T∙m/A
3.00×108 m/s
Mass of an electron
Mass of a proton
Permeability of Free Space
Speed of Light (vacuum)
f
q
virtual
Converging Mirror/Lens
p>f
real
p<f
virtual
real, inverted image
virtual, upright image
q
d sinθbright = m
Bright Fringes (Double Slit Interference)
g
Always
q
d sinθbright = m
L
ybright =
m
d
d sinθdark = (m + ½)
L
1
ybright =
(m + )
d
2
1
2t = (m + ) film
2
2t = mfilm
Lens Power
Diverging Mirror/Lens
p
WAVE OPTICS
upright
m
inverted
m
|𝑚| < 1
reduced image
|𝑚| > 1
enlarged image
Combinations of Lenses
m = (m1)(m2)
1
1 1
= +
𝑓𝑛𝑒𝑡 𝑓1 𝑓2
1
1 1
𝑑
= + +
𝑓𝑛𝑒𝑡 𝑓1 𝑓2 𝑓1 𝑓2
magnification
Two lenses in direct
contact
Two lenses not in direct
contact
Optical Instruments
M1 = −
𝑚𝑒 =
m=
≈
𝐿
𝑝1 𝑓𝑜
25𝑐𝑚
𝑓𝑒
θ
𝑓𝑜
=
θo 𝑓𝑒
θ𝑚𝑖𝑛 ≈
θ𝑚𝑖𝑛
𝑞1

𝑎
1.22
≈
𝐷
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Lateral magnification of
objective
Angular magnification of
eyepiece
Angular magnification of
a telescope
Telescope Resolution
(Single Slit)
Telescope Resolution
(circular aperture )
5
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