L3FA11 - P123Lecture317Sept2010 Motionin2 and3Dimensions...

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1 P123 Lecture 3 17 Sept 2010 Motion in 2 and 3 Dimensions REVIEW OF 1-D MOTION • For CONSTANT acceleration in 1-D • Free Fall: replace with ; 1 2 x x x ; t x av x v dt dx t x t x v 0 lim dt dv t v t x x x a 0 lim t v x x av a 2 2 1 at t v x x x o o 2 ; x o x x o x v v av t x x av v v a v v o x o x x x 2 2 2 ) (   x a   y g
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2 i Clicker!!
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3 MOTION IN 2 AND 3 DIMENSIONS Recall: Displacement is a vector ! • Has magnitude and direction So are velocity and acceleration • Represent vector by arrow: Here: (Same magnitude and direction) Do not need to lie on top of each other Furthermore: (Same Magnitude, Opposite Direction) Notation: = Magnitude of vector Write: = A NOTE: For vectors above: | | = B = A and | | = C = A ! ( - sign indicates direction) A B A C   B | | A | | A A B C A B C
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4 VECTOR ALGEBRA Given: What is ? Consider displacement, first by then by : Net displacement is Geometrical addition by “ head to tail ” method. • Consider parallelogram: • But we can also do: Vector addition is commutative: B A A B R R B A R B A R A B R B A A B A B A B R A R B A B R is the diagonal
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5 ) ( B A B A Subtraction: Notice : is vector from tip of
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L3FA11 - P123Lecture317Sept2010 Motionin2 and3Dimensions...

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