Final Exam Formulas P111 F2011

P mv f net δ t mv f mv i m 1 v 1i m 2 v 2i m 1 v 1f

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p = mv; F net Δ t = mv f – mv i m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f ; perf. inelastic: m 1 v 1i + m 2 v 2i = (m 1 + m 2 ) V elastic coll.: i 2 2 1 2 i 1 2 1 2 1 f 1 v m m m 2 v m m m m v + + + - = , i 2 2 1 1 2 i 1 2 1 1 f 2 v m m m m v m m m 2 v + - + + = rotational motion: 1 rev = 2 π rad; ω = ω 0 + α t; θ = ω 0 t + 2 t 2 1 α ; α ω - ω = θ 2 2 0 2 s = θ r v = ω r; a t = α r τ = rFsin φ ; τ net = I α ; work: W = τ θ ; W = 2 i I 2 1 2 f I 2 1 ω - ω P avr = t W Δ I point mass = mr 2 I disk,cyl = 2 mR 2 1 I hoop = mR 2 I rod = 2 mL 12 1 I rod(end) = 2 mL 3 1 I ball = 2 mR 5 2 I shell = 2 mR 3 2 I = I com + MD 2 Rolling: v com = R ω K = 2 I 2 1 ω + m 2 1 v com 2 Angular momentum: L r point mass = m r r x v r L = mrvsin θ ; L r =m ( r x v y r y v x ) k r L = I ω L I = L f Equilibrium: Σ F r = 0 : Σ τ r = 0 G = 6.67x10 -11 Nm 2 /kg 2 R E = 6.37x10 6 m , M E = 5.98x10 24 kg 2 2 1 R m m G F = 2 R p M G g = ; R m M G U o E - = ; R v m R m m G 2 2 2 1 = ; period T = v R 2 π ; R GM 2 v p esc = R GM v p sat = ; ; R GM 4 T 3 2 2 π = R 2 m M G E o E sat - = Oscillations: F = -kx x = Acos( ω t+ ) v = - ω A sin( ω t+ ) a = - ω 2 x ω = 2 π f = T 2 π ω = m k period: T spring = k m 2 π ; f = T 1 T pend = g L 2 π T phys.pend = mgd I 2 π U spr = ½ kx 2 E tot =½ kA 2 E tot =½kx 2 + ½mv 2 v max = A ω a max = A ω 2 2 1 2 2 1 1 cm m m x m x m x + + = 2 1 2 2 1 1 cm m m y m y m y + + =
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  • Fall '09
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