exam-1-eqsheet

# exam-1-eqsheet - Some Equations for Exam 1 1 2 sin 30 = sin...

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Some Equations for Exam 1 sin 30 = 1 2 =0 . 50; cos 30 = 3 / 2 ± 0 . 87 sin 60 = 3 / 2 ± 0 . 87; cos 60 = 1 2 . 50 sin 45 = 2 / 2 ± 0 . 71; cos 45 = 2 / 2 ± 0 . 71 For vectors ± A = A x ˆ i+ A y ˆ j+ A z ˆ k and ± B = B x ˆ B y ˆ B z ˆ k: | ± A | = A = ± A 2 x + A 2 y + A 2 z ; ± A · ± B = AB cos θ = A x B x + A y B y + A z B z ; ± A × ± B =( A y B z - A z B y ) ˆ i+( A z B x - A x B z ) ˆ j+( A x B y - A y B x ) ˆ k; | ± A × ± B | = AB sin θ . For a function of the form f ( x )= ax n , where n is an integer, df dx = nax n - 1 and ² f ( x ) dx = a n +1 x n +1 + C . If a particle’s position is represented by ±r = ( t ), ±v = d±r dt and ±a = d±v dt = d 2 dt 2 . Therefore, v x ( t ³ a x ( t ) dt + C and x ( t ³ v x ( t ) dt + C , and similarly for y - and z -components. For a constant acceleration , ( t 0 + 0 t + 1 2 ±a t 2 and ( t 0 + where 0 and 0 are the position and velocity at time t = 0, respectively.
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## This note was uploaded on 07/30/2008 for the course PHY 317k taught by Professor Kopp during the Spring '07 term at University of Texas at Austin.

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