Physics 101 Formulas

Kinematics
v
ave =
Dx/Dt            aave = Dv/Dt  
v = v0 + at                 x = x0 + v0t + 1/2at2         v2 = v02 + 2a
Dx            
g=9.81m/s2 = 32.2ft/s2

Dynamics
SF = ma                   Fg = Gm1m2 / R2            Fg = mg (near earths surface)
fs,max =
msFN                   fk = mkFN
ac = v2 / R =
w2R

Work & Energy
WF = FScos(
q)        KE = 1/2mv2      WNET = DKE = KEf - KEi
Wnc =
DE = Ef - Ei = (KEf + PEf) - (KEi + PEi)
Wgrav = -mg
Dy   PEgrav = mgy

Impulse & Momentum
Impulse I = Fave
Dt = Dp        FaveDt = Dp = mvf - mvi           Fave = Dp/Dt
SFext Dt= DPtotal  = Ptotal,final - Ptotal,initial     (momentum conserved if SFext = 0)
Xcm = (m1x1+ m2x2) / (m1+m2)

Rotational Kinematics
w = w0 + at                 q = q0 + w0t + 1/2at2         w2 = w02 + 2aDq  
vT =
wR    aT = aR   ( so for rolling without slipping v = wR    a = aR )

Rotational Statics & Dynamics
t = FL (L is lever arm= distance from line of force to rotation axis)
St = 0 and SF=0  (static equilibrium)
St = Ia
I = S
mr2   (for a collection of point particles)
I =1/2MR(solid disk or cylinder)       I =2/5MR(solid sphere)        I =2/3MR(hollow sphere)  
I =MR(hoop)
W =
tq    (work done by a torque)
L =
Iw           Stext Dt = DL     (angular momentum conserved if Stext = 0)
KE
rot=1/2Iw2  =L2/2I       KEtotal=KEtrans + KErot = 1/2mv2 + 1/2Iw2





Simple Harmonic Motion
Hookes Law:  Fs= -kx
Wspring = 1/2kxi2 - 1/2kxf2   PEspring = 1/2kx2
For a mass on a spring  x(t) = Acos(
wt)   or   x(t) = Asin(wt)
w2 = k/m,  T = 2p/w, f = 1/T
xmax= A        vmax= wA      amax= w2A
For a simple pendulum 
w2 = g/L

Fluids
P2 = P1 + rg(y1-y2)  change in pressure with depth
Buoyant force
FB = rgVdis = weight of displaced fluid
Flow rate Q = v
1A1 =  v2A2      continuity equation   (area of circle A = pr2)
P1 + 1/2rv12 + rgy1 = P2 + 1/2rv22 + rgy2    Bernoulli equation
rwater = 1000 kg/m3   1m3 = 1000 liters
r = M/V