Physics C Formulas Kinematics Rotational Dynamics Uniform by cdc16374

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									                                Physics C Formulas

Kinematics                                       Rotational Dynamics
Uniform Acceleration:                             τ = rFsinθ
V= Δ x / t                                        I = mr2 (point mass) = ( ) mr2
a= Δ v / t                                        I = Icm + mh2
x = xo + vo + 1/2at2                              I = ∫ dmr2 = ∫ (m/L) dx x2
v = vo + at                                      α = τ net / I
vf2 = vo2 + 2a Δ x                               k = ½ I ω2
x = v t = [ (v + vo)/2 ] t                       Angular Momentum
Non uniform Acceleration:                         L=Iω
v = dx/dt                                         L = m v r closest
a = dv/dt                                         Li = Lf
Δ x = ∫ v(t) dt                                   SHM
∆ v = ∫ a(t) dt                                   x = A sin ωt
Newton’s Laws                                     v = A ω cos ωt
Fnet = ma (2nd law)                               a= - A ω2 sin ωt
Ff = μ Fn                                         ω= 2π / T
Fs = k x                                         Mass on a Spring
Differential Equations                            d2x/dt2 = - kx/m
a = Fnet / m à dv/dt = Fnet / m                    ω = √ k/m
Work                                              T = 2π √ m/k
w = Fd cos θ = F ∙ x                              Total Energy = k + Us = ½ KA2
w = area under F- x curve                         Pendulum
w = ∫ F(x) dx                                      T=2π √ L/g
Power “rate of change of energy”                   Torsion Pendulum
Pavg = w / t                                       T = 2π √ I/κ
P = dw /dt                                        Gravitation
w = ∫ P(t) dt                                      outside planet
P = F v cos θ                                      Fg = (Gm1m2)/r2
Energy                                             g = (Gm) / r2
k = ½ mv2                                         Ug = - (Gm1m2) /r
Ug = mgh                                           inside planet
Us = ½ k x2                                       g = (4/3) Gρπ rinside
∆k=w                                              Circular Orbits
∆ u = w = - ∫ F(x) dx                             Fc = Fg à mv2/r = Gm1m2/r2
Energy i = Energy f                               ac = g à v2/r = GM/r2
Potential Energy Curve                             v = √ GM/r
F = - du/dx = - slope of u function                Elliptical Orbits
Center of Mass                                    T2= (4π2/GM) r3
Xcm = (X1m1 + X2m2 + …) / (m1+m2+…)                 ki + Ugi = Kf + Ugf
Xcm = (1/m) ∫ λ x dx       λ = mass/ length        at extremities
Impulse                                          Li = Lf à mvr = mvr
p = mv
J = ∆p
J = Favg t
J = area under F-t curve
J = ∫ F(t) dt

Momentum Conservation                   Kirchhoff’s Rule
Pi = Pf isolated system                  Junction: Iin = Iout
Rotational Kinematics                   Loop: Σ ∆V = 0
ω = θ / t = dθ/dt                       Charging Capacitors
α = ∆ω/ t = dω/dt                       q= ξ C (1- e–t/RC)
θ = θo + ωot + ½ αt2                    I = (ξ / R ) e–t/RC
ω = ωo + αt                             τ = RC
ω2 = ωo2 + 2 α ∆θ                      Discharging Capacitors
θ = s/r                                 q = Qo e–t/RC
ω = v/r                                  I = (V/R) e–t/RC
α = a/r                                  I = dq/dt à q = ∫ I(t) dt
Electrostatics                          Magnetism
F = KQ1Q2/r2                            on particles
Fe = qE                                  FB = q v B sinθ = q v x B
Point Charge                            on short wires
E = KQ/r2                               FB = BIL sinθ
Smooth Charge Distribution              on long wires
dE = (Kλdx) / (x2+R2) à dEx = dEcosθ    B = μo I / 2π r
Guass’s Law                             Biot-Savart Law: Short Wires
Φ = ∫ E dA                              dB = (μo I ds / 2π r2) sinθ
 ∫ E dA = qenc/ εo                     Ampere’s Law
Potential vs. Potential Energy           ∫ B ds = μo Ienc
∆ v = Eavgd                            Flux
∆ v = - ∫ E ds                         Φ = BconsA cosθ = B ∙ A
E = - dv/dx                            Φ = ∫ B(x) w dx
∆ Ue = qV                               Induction
Charge Distribution                      ξ = -dΦ/dt
V = KQ/r (pt. charge)                    ξ = BLv
Ue = KQ1Q2/r (pt. charge)               Inductance
(smooth)                                 ξ = -L (dI/dt)
V = KQ/R                                 L=NΦ/I
Capacitor                               Solenoid
C = Q/V                                  L/l = μo n2 A
Uc = ½ QV = ½ CV2 = ½ Q2/C              RL Circuits
Parallel Plate                            I = (ξ/R )(1- e–Rt/L) à with emf
E = - σ / εo = Q/A εo                    I = Io e–Rt/L à without emf
V = Ed                                   τ = L/R
C = A εo / d                            Maxwell’s Equations…4/3 notes
Circuits
I = ∆ q / t = dq/dt
R = ρ L / A = L/ σ A à ρ = 1/σ
Ohm’s Law
V = IR
J = I/A= σE
P = IV = I2R = V2/R

								
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