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Translational motion (v as function of initial v, a and x)


v2=vo2+2a(x)


Impulse
Imp=FavgΔt

inelastic collision (Conservation Laws)
Ρinitial=Pfinal


elastic collision (Conservation Laws)
Pinitial=Pfinal
Kinitial=kfinal


specific gravitiy (ie. relative density)
Þsubstance/Þwater
Pressure in liquid
P=rho*g*y
bouyant force
Fbouy=rhofluid*V*g

Bernoulli''s equation
K=P+½Þv2+Þgh

v=√2gh
beat frequency
| f1-f2 |

Electric field


E=kq/r2
ohms law
V=iR
power (electric)
P=iV
Capacitance
C=Q/V

focal point of a spherically curved mirror
f= -½r
index of refraction
n=c/v
Snell''s Law

n1sinø1=n2sinø2

or
sinø1/sinø2 = v1/v2 = n2/n1



Optical Power of Lens



Measured in?
optical power= 1/f



(Measured in diopters, ie m-1)
Thin Lens Formula
(relating the distance to image with focal length and distance to object)


1/f=1/do+1/di


magnification


m=-di/d0 or hi/ho


units of pressure


1atm=760torr=105pascals

Phase Velocity of shallow water waves

Of deep water waves
vp=√(gh)  (shallow)

vp=√(gλ/2*pi)   (deep)

Lorentz Transformation for time

t'' = γ(t-vx/c2)
Lorentz Transformation for velocity, ux''


ux'' = ux - v / (1 - v*ux/c2)



Lorentz Transformation for velocity, uy''






uy'' = uy / γ(1 - v*ux/c2)



Equation for time w/r to proper time


Δt = γτ

Equation for length w/r to proper length


L = Proper length / γ

Classic Doppler effect (with receiver chasing the source)


f=(v + vr)*(v + vs)-1 f0



Relativistic Doppler Effect, approaching (source and observer moving toward each other with v)


f = (1+beta)1/2(1-beta)-1/2 f0


Relativistic Doppler Effect, receding (source and observer moving toward each other with v)


f= (1-beta)1/2(1+beta)-1/2 f0


Redshift (z)


z = (f0 - f) / f

Lorentz Transformation for Acceleration (ax'')


ax'' = ax / γ3(1 -v*ux/c2)3


Headlight Effect (half the light concentrated to cone of θ w/r to β)


θ = cos-1(β)

Relativistic Momentum
p = γmu




(A Conserved quantity)
Lorentz Transformation for Energy


E'''' = γ(E - vpx)

Lorentz Transformation for px''


px'' = γ(px - vE/c2)

Lorentz Transformation for py''


py'' = py


Solar Constant
1400 W/m2




Intensity of sun''s rays on Earth
Charge of the Electron


e = 1.6 * 10-19 C

(1 eV = 1.6 * 10-19 J)
Mass of unbound Proton/Neutron (in MeV/c2)


Proton: 938 MeV/c2


Neutron: 940 MeV/c2
Energy of massless particle w/r to momentum
E = pc
Energy-momentum four-vector


(mc2)2 = E2 - (pc)2


1 Unified Atomic Mass Unit in MeV/c2

In kg?


930 MeV/c2

1.66 * 10-27 kg
Rest Energy of Muon
105.7 MeV
Rest Energy of Electron
0.511 MeV
Useful Equations
u/c = pc/E
E≈pc, for E»mc2


Schwartzchild Radius (Rs)


Rs = 2GM / c2


Rs of sun
~3km
Gravitational Redshift (source at R, observer at ∞)


f = (1-GM/c2R)f0


Gravitational Blueshift (source at infinity, observer at R)


f = (1+GM/c2R)f0


Escape Velocity


ve= √(2GM/R)

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