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APPhys Equations

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force required to keep an object moving along a circular path (centripetal force)
F(c) = mv²/r
velocity and displacement relationship of an accelerating object
v² = v₀²+2ax
displacement and time relationship of an accelerating object
x = ½at²+v₀t
equivalence between energy and mass
E₀ = mc²
kinetic energy of electrons in the Photoelectric Effect measured from the Stopping Potential
KE(max) = eV₀
energy involved in the photoelectric effect
hf = ϕ + KE (max)
wavelength of a particle
λ=h/p
momentum of a photon
p = E/c
energy of a photon
E=hf
approximation for small angles in Double and Single Slit experiments
sinθ≈y/L
angular position of a dark fringe in a Single Slit Experiment
asinθ=nλ
n= 1, 2, 3,...
angular position of a dark fringe in a Double Slit Experiment
dsinθ= nλ/2
n = 1, 3, 5,...
angular position of a bright fringe in a Double Slit Experiment
dsinθ= nλ
n = 1, 2, 3,...
magnification of an object based on the object and image distances from a mirror or lens
M= -d(o)/d(i)
relationship between object and image distances from a mirror or lens
1/f = 1/d(o) + 1/d(i)
minimum incident angle that will result in total internal reflection
sinθ(c)=n₂/n₁
relationship between incident and refracted angles of light rays (Snell's Law)
n₁sinθ₁=n₂sinθ₂
relationship between the wavelengths of a wave in different media
λ₁n₁=λ₂n₂
definition of index of refraction
n = c/v
relationship between incident and reflected angles of light rays
θ₁=θ₂
path difference required to create destructive interference
∆L = nλ/2
n = 1, 3,5, ...
path difference required to create constructive interference
∆L = nλ
n = 1, 2, 3,...
frequency required to create standing waves with one closed and one open end (air column)
f(n) = nv/4L
n = 1, 3, 5,...
frequency required to create standing waves with two closed (string) or two open ends (air column)
f(n) = nv/2L
n = 1, 2, 3, ...
physical factors that determine the speed of a wave on a string
v=√(T/μ)
frequency perceived by an observer due to the Doppler Effect
f₀=f(s)(v±v(o)/v-+v(s))
relationship between the frequency, wavelength, and speed of a wave
v=λf
equation of a simple harmonic oscillator
x=Asin(ωt)
physical factors that determine the period of a pendulum
T=2π√(l/g)
physical factors that determine the period of a mass-spring system
T=2π√(m/k)
relationship between the frequency and angular frequency of an oscillator
ω=2πf
relationship between the frequency and period of an osciallator
f=1/T
force due to a spring
F(s) = kx
emf cased by a square loop with a movable side (motional emf)
E=vBl
emf caused by a changing flux about a loop (Faraday's Law)
E=(N)∆Φ/∆t
magnetic flux about a loop
Φ=BAcosθ
magnetic force on a current
F = IBlsinθ
magnetic force on a moving charge
F = qvBsinθ
magnetic field created by a wire loop
B=μ₀I/2r
magnetic field created by a straight wire
B=μ₀I/2πr
energy stored in a capacitor
U = ½QV=½CV²=½Q²/C
charge on a capacitor caused by a potential difference
Q=CV
physical factors that determine capacitance
C=ε₀A/d
power dissipated by a resistor
P=IV=V²/R=I²R
current through a resistor caused by a potential difference in a circuit (Ohm's Law)
I=V/R
current is defined as charge passing in a given amount of time
I=∆Q/∆t
physical factors that determine resistance
R=ρl/A
potential difference between 2 points in an electric field
∆V=-Ed
potential energy of a two charge system
U = kq₁q₂/r²
potential produced by a point charge
V = kq₁/r
potential energy of a point charge in a potential
U = Vq₂
force on a charge in a field
F(E) = Eq₂
force between two charges (Coulomb's Law)
F(E) kq₁q₂/r²
electric field produced by a point charge
E =kq₁/r²
horizontal force due to a surface while counteracting a force (static friction)
F(s) ≤ μN
gravitational potential energy of a object on the surface of a planet
U = mgh
potential energy and work relationship
∆U ≡ -W
power associated with a force applied to an object moving at constant velocity
P= Fv
power associated with a change in energy
P = ΔE/Δt
work done by a constant force
W ≡ Fd (parallel)
torque applied by a lever arm
τ ≡ Fr (perpendicular)
acceleration due to Gravity on a surface of a planet
g = Gm/r²
gravitational force between two objects (Newton's Law of Gravitation)
F(g) = Gm₁m₂/r²
acceleration of an object moving along a circular path (centripetal acceleration)
a(c) = v²/r
power associated with work done
P = W/t
Momentum of an object
p ≡ mv
Impulse applied to an object
I ≡ F(Δt)
force due to a planet's gravity (Weight)
w = mg
horizontal force due to surface while counteracting a force (static friction)
F(s) ≤ μ(s)N
horizontal force due to a surface while sliding (static friction)
F(k) = μ(k)N
Kinetic Energy of an object
KE ≡ ½mv²
change in energy caused by work (Work-Kinetic Energy Theorem)
W=∆KE
change in momentum due to an impulse (Impulse-Momentum Theorem)
I = ∆p
velocity and time relationship of an accelerating object
v = v₀ + at
acceleration caused by a net force on an object (2nd Law)
a = F(net)/m
displacement and time relationship of an object in constant velocity
x = vt
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