Exam Formulae

Exam Formulae - r = ˙ θ ˆ θ d dt ˆ θ =-˙ θ ˆ r...

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On the exam paper, the formulae occupy more than one page. Formula Sheet Constant acceleration v f = v i + at x - x 0 = v i t + 1 2 at 2 v 2 f = v 2 i + 2 a ( x - x 0 ) Newton’s Laws etc. ± p = m±v ± F = m±a = d dt ± p ± F 12 = - ± F 21 E = K + U K = 1 2 mv 2 U = mgx U = - GMm/r U = 1 2 kx 2 X CofM = ( m 1 x 1 + m 2 x 2 ) / ( m 1 + m 2 ) V CofM = ( m 1 v 1 + m 2 v 2 ) / ( m 1 + m 2 ) K = K ± + K CofM ± F ext = d dt ± P X ± p ± = 0 Calculus of physics d dt x = v x ˙ x d dt ± r = ±v d dt v x = a x ˙ x d dt ±v = ±a a x = v x dv x dx W = Z Fdx W = Z ± F · ± dr F x = - dU dx ≡ - U ± ( x ) F x = d dt p x ± F = d dt ± p Oscillatory motion ω 0 = q k/m ω 0 = q U ±± /m Resistive motion F = - mkv F = - mDv | v | continued, next page . . . 1
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Reference Frames x ± = x - V t v ± = v - V a ± = a - A F fict = - mA Special Relativity γ = [1 - β 2 ] - 1 2 with β = v/c Lorentz transform: x ± = γ [ x - vt ]; t ± = γ [ t - vx/c 2 ] x = γ [ x ± + vt ± ] t = γ [ t ± + vx ± /c 2 ] Lorentz contraction: Δ x = Δ x ± Time dilation: Δ t = γ Δ t ± u x = u ± x + v 1 + vu ± x /c 2 u y = u ± y 1 + vu ± x /c 2 ± p = γm 0 ±v E = γm 0 c 2 m 2 0 c 4 = E 2 - p 2 c 2 λ = λ ± s 1 - β 1 + β Rotational motion ±v = ± r × ±ω ± G = ± r × ± F ± ² = ± r × ± p ± G = d dt ± ² ± L = X ± ² = I±ω I = X mr 2 Z V r 2 dm I C = X m | ± r - ± R C | 2 ± L C = I C ±ω K ± = 1 2 I C ω 2 d dt ± L C = ± G ext Polar coordinates ± r = r ˆ r ±v = ˙ r ˆ r + r ˙ θ ˆ θ ±a = [¨ r - r ˙ θ 2 r + [ r ¨ θ + 2 ˙ r ˙ θ ] ˆ θ d dt ˆ
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Unformatted text preview: r = ˙ θ ˆ θ d dt ˆ θ =-˙ θ ˆ r Coriolis and Centrifugal . . . ±a =-2 ±ω × ±v-±ω × ( ±ω × ± r ) ±a =-2 ω [ v r ˆ θ-v θ ˆ r ] + ω 2 r ˆ r Calculus and other math Z dv v-v = ln | v-v | + constant Z vdv Av 2 ± B = 1 2 A ln | Av 2 ± B | + constant f ( x-x ) ² f ( x )+ f ± ( x )( x-x )+ 1 2 f ±± ( x )( x-x ) 2 + ··· e-a ² 1-a + 1 2 a 2 . . . a ³ 1 sin a ² a-1 6 a 3 . . . a ³ 1 cos a ² 1-1 2 a 2 . . . a ³ 1 If b = e a then a = ln b (1-p ) q ² 1-qp + 1 2 q ( q-1) p 2 + ··· p ³ 1 2...
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This note was uploaded on 04/29/2008 for the course PHYS 230 taught by Professor Harris during the Fall '07 term at McGill.

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Exam Formulae - r = ˙ θ ˆ θ d dt ˆ θ =-˙ θ ˆ r...

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