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Kinematics (Linear and projectile motion)

Kinematics (displacement vs. distance, average velocity vs. average speed, acceleration)
Displacement is the change in position independent of path length
Distance is the length of the path
Average velocity is displacement over time
Average speed is distance over time
Acceleration is v/t

Work and Power
 W=Fdcosθ
 Wnet=ΔKE
 If force is perpendicular to displacement, work is zero
 Power = W/t or Fvcosθ

Kinetic Energy, Potential Energy, Total mechanical Energy, Mechanical Advantage, Workenergy theorem, conservation of energy, mechanical advantage
 KE=1/2*mv^2
 PE=mgh
 E=PE+KE
 W(total)=ΔKE
 KE+PE(initial)=KE+PE(final)
 Increase distance causes a lower force

Momentum, impulse, conservation of momentum, elastic collision, inelastic collision, perfectly inelastic collision
 p=mv
 J=F(average)t=Δp
 p(initial)=p(final)
 KE(initial)=KE(final)
 KE(initial) doesn't = KE(final)
 Objects stick and move together

Newton's Laws
A body in motion is stay in motion (same for rest) unless acted upon by a net force
A body will be accelerated in the same direction of the net force applied to it (F=ma)
All forces are equal and opposite in direction
All matter experience attractive force

Frictional forces (Static, Kinetic, centripetal)
0≤f_{s}≤μ_{s}F_{N}
f_{k}=μ_{k}F_{N
}A_{c}=v^{2}/r
F_{c}=mv^{2}/r

Center of mass and torque
X_{cm}=(m_{1}x_{1}+m_{2}x_{2}+...)/(m_{1}+m_{2}+...)
τ=rFsinθ=lF
r_{1}mgsinθ=r_{2}Fsinθ

Fluids (density, specific gravity, weight, absolute pressure, gauge pressure)
ρ=m/V
ρ _{substance}/ρ _{water
}ρgV
P=F/A
 Absolute pressure = atmospheric pressure (typically 10^{5} Pa) + ρgh
 Gauge pressure = absolute pressureP_{atm}

Buoyant Force, Floating objects, Flow rate, continuity equation, Bernoulli's equation, Pascal's principle, velocity, relationships
F_{b}=ρgVsubmerged
Fractions of floating object that is submerged = ρ_{object}/ρ_{fluid}
A_{1}v_{1}=A_{2}v_{2}
P+1/2ρv^{2}+ρgh (for state 1)=P+1/2ρv^{2}+ρgh
ΔP=A_{1}F_{2}=A_{2}F_{1} and W=F_{1}h1=F_{2}h_{2
}velocity inverse with area and pressure

Coulomb's Law, Electric field, Electric potential, Potential difference, Electric potential energy
F=kq_{1}q_{2}/d^{2
}E=F/q=kq/d^{2
V=kq/dU=qΔV=kq1q2/d
}

Current, Ohms Law, Power, Resistance
Current is the flow of electric charge; opposite of electron flow, electrons flow from negative terminal through circuit to positive terminal)
V=IR
P=IV=I ^{2}R=V ^{2}/R

Series circuits
R_{eq}=R_{1}+R_{2}+R_{3}+...
I=I_{1}=I_{2}=I_{3}=...
V=V_{1}+V_{2}+V_{3}+...

Parallel circuits
R_{eq}=(R_{1}+R_{2}+R_{3}+...)^{1
}I=I_{1}+I_{2}+I_{3}+...
V=V_{1}=V_{2}=V_{3}=...

Capacitance, Energy stored, Equivalent capacitance
C=Q/V (farad)
PE=1/2QV=1/2CV^{2}=1/2Q^{2}/C
Adding dielectric increases capacitance
Series: C_{eq}=(C_{1}+C_{2}+C_{3}+...)^{1}
Parallel: C_{eq}=C_{1}+C_{2}+C_{3}+...

Magnetic force on charge+RH rule, force on currentcarrying wire + RH rule, magnetic field
F_{B}=qvBsinθ (fingers in B, thumb in v, palm is F_{B})
qvB=mv^{2}/r
F_{B}=ILBsinθ (thumb points in direction of current, fingers curl in B)
B=μ_{0}I_{1}I_{2}/d (Tesla)

Period, Frequency, angular frequency, simple harmonic motion, mass spring (force, energy, frequency)
T=seconds/cycle
f=1/T or cycles/second
ω=2πf
Period and frequency are independent of amplitude
F _{s}=kx, PE=1/2kx ^{2},

Pendulum (frequency, at equilibrium, at amplitude)
Equilibrium: v is max, a = 0, KE is max, PE=0
Amplitude: v=0, a is max, KE=0, PE is max

Wavelength, Young's modulus, velocity, string attached at each end, open pipe, closed pipe
v=fλ
Young's Modulus = (F*L _{0})/(A*ΔL)
String: λ _{n}=2L/n (n=1,2,3...)
Open pipe: λ _{n}=2L/n (n=1,2,3...)
Closed pipe: λ _{n}=4L/n (n=1,3,5...)

Speed of sound relationships, intensity, Beats, Doppler effect
higher density = lower resistance to compression = lower spreed
f _{beat}=f _{1}f _{2}
(Vo is + if observer moves toward source; Vs is  if source moves toward observer, + on top and  on bottom if both coming closer)

Light, diffraction, refraction, snell's law
 lights is an electromagnetic wave that does not need a medium
 wsinθ=nλ (n=1,2,3...)
 n=c/v
 n1sinθ1=n2sinθ2 (n2>n1 light bends toward normal)

Mirrors
Spherical: Real images formed on same side as object; virtual images formed on side opposite of object
 Concave: f=r/2, CCMIBEV (ConCave Mirror Inside focal length image is Behind mirror, Enlarged, and Virtual)
 Convex: f=r/2, CVMVUO (ConVex Mirror Virtual Upright Only)

Lenses
Converging: f is positive, CVLBRI (ConVerging Lens Beyond focal point image is Real and Inverted) Diverging: f is negative, DVLVSSO (DiVerging Lens Virtual Image Only Sameside Smaller )

Mirror/lens equation, magnification equation
1/f=1/do + 1/di
m=i/o


