PHY “Physics with Calculus 1” Summer 2012Physical Constants and Formula Sheet (version of 26 July 2012)Professor Mark W. Meisel and Teaching Assistant Yan Wang

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may not be used to store/recall formula. The quizzes, tests, and final exam must be your own independent

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=====================================================g = 9.8 m

s2g = 32 ft

s21.00 in = 2.54 cm c = 2.998 × 108 m/s

G = 6.67 × 10−11 N · m2 / kg2

v = vo + at x − xo = vot + 1

2at2

v2 = v2o + 2a(x − xo)

x − xo = 1

2(vo + v)t x − xo = vt − 1

2at2

~a ·~b = axbx + ayby + azbz ~a ·~b = |~a| |~b| cos(θ)

|~a ×~b| = |~a| |~b| sin(θ) ~a ×~b = (aybz − azby )i + (azbx − axbz)j + (axby − aybx)k

~r = xi + yj + zk ~v = d~rdt

~a = d~vdt

R = v2o

gsin(2θo)

f = 1

Tω = 2π f ~a = −ω2 ~r a = v2

rv = ω r

~F = m~a fs ≤ µs FN fk = µk FN

K = 1

2mv2 ∆K = Kf − Ki = W W = ~F · ~d =

∫ fi F (x) dx

P = dWdt

= dEdt

~Fs = −k~d Fx = −kx∆U = mg(∆y) U(x) = 1

2kx2 W = ∆E ∆E = ∆Emec + ∆Eth + ∆Eint

~rcom = 1

M

∑i mi~ri M =

∑i mi

~Fnet = M ~acom

~p = m~v ~Fnet = d~p

dt~J = ∆~p ~J =

∫ fi

~F (t) dt~P = M ~vcom

~Fnet = d~Pdt

~Pi = ~Pf ∆Kelastic = 0R vrel = Ma vf − vi = vrel ln( Mi

Mf)

s = rθ ω = dθdt

α = dωdt

ar = v2

r= rω2 at = rα

I =∑

i mir2i =

∫r2dm I = Icom + Mh2 ~τ = ~r × ~F τ = Iα

~L = ~r × ~p L = Iω ~Li = ~Lf ~τ = d~Ldt

K = 1

2Icomω2 + 1

2mv2

com W =∫

τdθ P = τω~Fnet = 0 and ~τnet = 0 in equilibrium. F = G m1 m2

r2

FA

= E ∆LL

FA

= G ∆xL

p = FA

= B ∆VV

U = −G m1 m2

r

ρ = mV

p2 = p1 + ρg(y1 − y2) Fb = mfg Rv = Av = “C”Rm = ρRv = ρAv = “C” p + 1

2ρv2 + ρgy = “C”

x(t) = xm cos(ωt + φ) a = d2xdt2

= −ω2 x ω2 = km

or κI

or g

Lor mgh

I

k = 2πλ

v = λf = ωk

y(x, t) = ym sin(kx ∓ ωt + φ)I = P/A I = Ps/(4πr2) Io = 10−12 W/m2 β = (10 dB) log(I/Io)