phy2048 lecture05

phy2048 lecture05 - 3-8 The Cross Product Properties of...

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Unformatted text preview: 3-8 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 4-1: Given the initial and final position vectors, find the displacement vector. Sample Problem 4-2,3&4: Given position (x and y) as function of time, at a certain time, find Position Velocity Acceleration Sample Problem 4-5: Motion with constant acceleration in 2-D 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.

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phy2048 lecture05 - 3-8 The Cross Product Properties of...

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