Formula Sheet

35 downloads 2605 Views 54KB Size Report
Physical Constants and Formula Sheet (version of 26 July 2012). Professor ... The quizzes, tests, and final exam must be your own independent work. Unless ...
PHY “Physics with Calculus 1” Summer 2012 Physical Constants and Formula Sheet (version of 26 July 2012) Professor Mark W. Meisel and Teaching Assistant Yan Wang PLEASE note these general rules for graded quiz material. Use only pencil. Show all work for full credit. Work must be clear and unambiguous for credit. Please place your name and the “last-4” of your UFID on the upper right-hand corner of your quiz. Calculators may be used for numerical work, but they may not be used to store/recall formula. The quizzes, tests, and final exam must be your own independent work. Unless otherwise stated, the notation is the same as used in lecture and the textbook. Please do not share quiz and small group work with students in other discussion sections until Thursday morning.

Recall that by participating in the graded work, you agree to abide by the the UF Honor Code: “On my honor, I have neither given nor received unauthorized aid in doing this assignment.” ===================================================== g = 9.8 sm2 g = 32 sft2 1.00 in = 2.54 cm c = 2.998 × 108 m/s 2 G = 6.67 × 10−11 N · m2 / kg v = vo + at x − xo = vo t + 21 at2 v 2 = vo2 + 2a(x − xo ) x − xo = 21 (vo + v)t x − xo = vt − 12 at2 ~a · ~b = ax bx + ay by + az bz |~a × ~b| = |~a| |~b| sin(θ) ~r = xˆi + yˆj + z kˆ 1 T

~a · ~b = |~a| |~b| cos(θ) ~a × ~b = (ay bz − az by )ˆi + (az bx − ax bz )ˆj + (ax by − ay bx )kˆ ~v =

d~r dt

~a =

d~v dt

R =

vo2 g

ω = 2π f

~a = −ω 2 ~r

F~ = m ~a

f s ≤ µ s FN

f k = µ k FN

K = 12 mv 2 P = dW = dE dt dt ∆U = mg(∆y)

∆K = Kf − Ki = W F~s = −k d~ Fx = −kx 1 2 U (x) = 2 kx W = ∆E

f =

P

P

~rcom = M1 i mi~ri p~ = m ~v P~ = M ~vcom R vrel = M a

M = i mi p F~net = d~ dt ~ F~net = ddtP Mi vf − vi = vrel ln( M ) f

s = rθ R P I = i mi ri2 = r 2 dm ~ = ~r × p~ L 2 K = 12 Icom ω 2 + 21 mvcom F~net = 0 and F = E ∆L A L ρ = m V Rm = ρRv = ρAv = “C” x(t) = xm cos(ωt + φ) k = 2π λ I = P/A

ω =

dθ dt

L = Iω R W = τ dθ ~τnet = 0 F = G ∆x A L p2 = p1 + ρg(y1 − y2 )

sin(2θo )

F~net = M ~acom J~ = ∆~ p P~i = P~f

α = dω dt I = Icom + M h2 ~i = L~f L P = τω in equilibrium. p = FA = B ∆V V Fb = m f g

2

a = ddt2x = −ω 2 x v = λf = ωk I = Ps /(4πr 2 )

Io = 10−12 W/m2

a =

v2 r

v = ωr

R W = F~ · d~ = if F (x) dx

∆E = ∆Emec + ∆Eth + ∆Eint R J~ = if F~ (t) dt ∆Kelastic = 0

2

ar = vr = rω 2 ~τ = ~r × F~ ~ ~τ = ddtL

at = rα τ = Iα

F = G m1r2m2 U = −G m1rm2 Rv = Av = “C” p + 21 ρv 2 + ρgy = “C” k ω2 = m or κI or Lg or mgh I y(x, t) = ym sin(kx ∓ ωt + φ) β = (10 dB) log(I/Io )