v s = v 0s + a s Δt s = 1 2 a s Δt 2 + v 0s Δt + s 0 v s = ds dt a s = dv s dt v 2 s = v 2 0s +2a s Δs KINEMATICS v t = !r ! = d✓ dt ↵ = d! dt a t = ↵r CIRCULAR MOTION s = ✓r ⌃ ~ F = m~ a DYNAMICS ROTATION OF A RIGID BODY ⌧ = rF sin φ = rF ? = r ? F ` = I ! I hoop = MR 2 CONSERVATION LAWS I k = I com + Md 2 I log or disk = 1 2 MR 2 I baton = 1 12 ML 2 W ext = ΔK + ΔU + ΔE th U s (x)= 1 2 kx 2 I point = N X i m i r 2 i #» J = Z t 2 t 1 #» F (t)dt = F avg Δt #» ` i = #» ` f #» ` = #» r ⇥ #» p = m( #» r ⇥ #» v ) #» ⌧ net = I #» ↵ #» F spring = -k #» x #» p = m #» v #» F A on B = - #» F B on A #» J = Δ #» p a r = a centrip = v 2 r = r! 2 #» p i = #» p f K trans = 1 2 mv 2 f s μ s n f k = μ k n K rot = 1 2 I ! 2 I sphere = 2 5 MR 2 I pipe = 1 2 MR 2 1 + R 2 2 SIMPLE HARMONIC MOTION T = 1 f ! =2⇡f x(t)= A cos(!t + φ 0 ) v(t)= -!A sin(!t + φ 0 )= -v max sin(!t + φ 0 ) ! spring = r k m ! pendulum = r g L ! phys-p = r Mgl I x(t)= Ae -bt 2m cos(!t + φ 0 ) ⌧ = m b TRAVELING WAVES D(x, t)= A sin(kx - !t + φ 0 ) β = (10dB) log 10 ⇣ I I 0 ⌘ f ± = f 0 1 ⌥ v s /v f ± = (1 ± v o /v)f 0 λ 0 = λ 0 s 1 ± v s /c 1 ⌥ v s /c D net = P i D i D(x, t)= A(x) cos !t =2a sin kx cos !t f beat = f 2 - f 1 ! damp = q ! 2 0 - b 2 4m 2 E = 1 2 mv 2 + 1 2 kx 2 = 1 2 kA 2 = 1 2 m(v max ) 2 Δφ destr. =2⇡ Δr λ + Δφ 0 = ( m + 1 2 ) 2⇡ Δφ const. =2⇡ Δr λ + Δφ 0 = m · 2⇡ v = λ T = λf k = 2⇡ λ n = c v λ m = 2L m I = P a v string = p T s /μ I 1 /I 2 = r 2 2 /r 2 1 1 1 p 2 45 ◦ 45 ◦ p 3 1 2 60 ◦ 30 ◦ a b p a 2 + b 2 ✓ g =9.8066 m s 2 c =2.99782 ⇥ 10 8m s tan ✓ ⇡ sin ✓ ⇡ ✓ (small ✓) n air =1.003 n water =1.33 n glass =1.5 I 0 = 10 -12 W m 2 tan ✓ = b a v sound = 343 m s PHYSICS 132 MIDTERM 2 EQUATION SHEET OPTICS n = c v λ = λ 0 n ✓ i = ✓ r n 1 sin ✓ 1 = n 2 sin ✓ 2 sin ✓ crit = n 2 n 1 f = R 2 1 s + 1 s 0 = 1 f m = h 0 h = - s 0 s n 1 s + n 2 s 0 = n 2 - n 1 R d sin ✓ m = mλ a sin ✓ p = pλ d sin ✓ m = ( m + 1 2 ) λ 1/f =(n - 1) ⇣ 1 R 1 - 1 R 2 ⌘