Final Exam Formulas P111 F2011

Final Exam Formulas P111 F2011 - PHYS 111 FINAL EXAM...

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PHYS 111 FINAL EXAM FORMULAS - FALL 2011 Vectors: A x = A cos θ ; A y = A sin θ ; A = 2 y 2 x A A + θ = tan -1 x A y A ; A r =A x i r + A y j r B A r r + = (A x + B x ) i r +(A y + B y ) j r A r · B r =A·Bcos θ = A x B x + A y B y A r x B r = ABsin θ = (A x B y - A y B x ) k r One-dimensional motion: x = v avr t t 2 v v x 2 1 + = x = v o t + 2 1 at 2 a 2 v v x 2 0 2 - = v = v o + at; Free-fall: y = v o t - 2 1 gt 2 , v = v o - gt, g 2 v v y 2 o 2 - - = ; g 2 v y 2 0 max = r = r 0 + (v ox t + 2 1 a x t 2 ) î + (v oy t + 2 1 a y t 2 ) ĵ v = (v ox + a x t) î + (v oy + a y t) ĵ ; Projectile motion: x = v ox t ; y = v oy t - 2 1 gt 2 ; v y = v oy - gt; v ox = v o cos θ ; v oy = v o sin θ ; g 2 v v y 2 oy 2 y - - = ; g v 2 t 2 y 0 tot = R= ; g 2 sin 2 o v θ 2 o 2 ) cos v ( 2 gx x ) (tan y θ - θ = F net = ma; F g = mg, g = 9.8 m/s 2 ; incline: F gx = mgsin θ , F gy = mgcos θ , Friction: f s,max = μ s N; f k = μ k N; Circular motion: a c = R v 2 ; period T = v R 2 π ; F net = mv r 2 ; work:
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