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Unformatted text preview: 38 The Cross Product Properties of Cross Products A A = 0 A B = B A A B + C = A B + A C d dB dA + A B = A B dt dt dt ( ) ( ) ( ) ( ) ^ j ^ i^=k ^k = i j ^ ^ ^ ^ j k i = ^ ^ ^ i = k j ^ ^ j ^ k ^ = i ^ ^ i k =  ^ j ^ ^ j j ^ ^ i i = ^ ^ = k k = 0 Properties of Cross Products C = A B C x = Ay Bz  Az B y C y = Az Bx  Ax Bz C z = Ax B y  Ay Bx ^ i C = A B = Ax Bx ^ j Ay By ^ k Az Bz Example ^ A = 3i + 2 ^ j ^ B = 4i  3 ^ j =? Chapter 4: Motion in Two and Three Dimensions
41 What is Physics 42 Position and Displacement 43 Average Velocity and Instantaneous Velocity 44 Average Acceleration and Instantaneous Acceleration 45 Projectile Motion 46 Projectile Motion Analyzed Chapter 4 Homework 1, 5, 7, 13, 15, 21, 24, 26, 31, 43, 57, 60, 63, 71, 78, 104, 114, 120 Displacement, Velocity, Acceleration Displacement r = r  r0 Velocity vavg Acceleration aavg r = t v = t dr v= dt 2 dv d r a= = 2 dt dt The x, y, and z parts of the motion are independent of each other Examples
Sample Problem 41: Given the initial and final position vectors, find the displacement vector. Sample Problem 42,3&4: Given position (x and y) as function of time, at a certain time, find Position Velocity Acceleration Sample Problem 45: Motion with constant acceleration in 2D Projectile Motion
Constant Acceleration: a =  g^ j ax = 0 v x = v0 x = constant x = v0 x t
ay = g v y = v0 y  gt 1 2 y = v0 y t  gt 2 2 v 2 = v0 y  2 gy y v0 x = v0 cos 0 v0 y = v0 sin 0 Projectile Motion Analyzed
Constant Acceleration: a =  g^ j ...
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This note was uploaded on 04/17/2008 for the course PHY 2048 taught by Professor Chen during the Fall '08 term at UNF.
 Fall '08
 Chen

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