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sy04_sept17_07hc - Physics 207 Lecture 4 Sept 17 Physics...

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Physics 207: Lecture 4, Pg 1 Physics 207, Physics 207, Lecture 4, Sept. 17 Lecture 4, Sept. 17 Agenda Agenda Assignment: Read Chapter 5 Assignment: Read Chapter 5 MP Problem Set 2 due Wednesday (should have started) MP Problem Set 2 due Wednesday (should have started) MP Problem Set 3, Chapters 4 and 5 (available soon) MP Problem Set 3, Chapters 4 and 5 (available soon) Chapter 3, Chapter 4 (forces) Chapter 3, Chapter 4 (forces) Vector addition, subtraction and components Vector addition, subtraction and components Inclined plane Inclined plane Force Force Mass Mass Newton’s 1 Newton’s 1 st and 2 and 2 nd nd Laws Laws Free Body Diagrams Free Body Diagrams
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Physics 207: Lecture 4, Pg 2 Vector addition Vector addition The sum of two vectors is another vector. A = B + C B C A B C
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Physics 207: Lecture 4, Pg 3 Vector subtraction Vector subtraction Vector subtraction can be defined in terms of addition. B - C B C B - C B - C = B + (-1) C A Different direction and magnitude !
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Physics 207: Lecture 4, Pg 4 Unit Vectors Unit Vectors A Unit Vector Unit Vector is a vector having length 1 and no units It is used to specify a direction. Unit vector u u points in the direction of U U Often denoted with a “hat”: u u = û U = |U| U = |U| û û û x y z i j k Useful examples are the cartesian unit vectors [ i, j, k i, j, k ] Point in the direction of the x , y and z axes. R = r x i + r y j + r z k
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Physics 207: Lecture 4, Pg 5 Vector addition using components: Vector addition using components: Consider C C = A A + B B . (a) C C = (A x i i + A y j j ) + (B x i i + B y j j ) = (A x + B x ) i i + (A y + B y ) (b) C C = (C x i i + C y j j ) Comparing components of (a) and (b) : C x = A x + B x C y = A y + B y C B x A B y B A x A y
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Physics 207: Lecture 4, Pg 6 Lecture 4, Lecture 4, Exercise 1 Exercise 1 Vector Addition Vector Addition Vector A = {0,2,1} Vector B = {3,0,2} Vector C = {1,-4,2} What is the resultant vector, D , from adding A + B + C ? A) A) {3,-4,2} {3,-4,2} B) B) {4,-2,5} {4,-2,5} C) C) {5,-2,4} {5,-2,4}
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Physics 207: Lecture 4, Pg 7 Lecture 4, Lecture 4, Exercise 1 Exercise 1 Vector Addition Vector Addition A. A. {3,-4,2} {3,-4,2} B. B. {4,-2,5} {4,-2,5} C. C. {5,-2,4} {5,-2,4} D. None of the above Vector A = {0,2,1} Vector B = {3,0,2} Vector C = {1,-4,2} What is the resultant vector, D , from adding A + B + C ?
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Physics 207: Lecture 4, Pg 8 Converting Coordinate Systems Converting Coordinate Systems In polar coordinates the vector R = (r, θ ) In Cartesian the vector R = (r x ,r y ) = (x,y) We can convert between the two as follows: In 3D cylindrical coordinates ( r , θ, z ), r
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