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3 Vectors in Physics 3-1 Scalars versus Vectors Scalar: a number with unit volume, time, temperature, distance … Vector: a mathematical quantity with both direction and magnitude velocity, acceleration, displacement …

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(1)Vector: draw diagram or sketch Magnitude: length of line Direction: arrow (2) Vector: write Boldface, r Draw arrow over the vectors symbol Magnitude: r=|r|=| | θ x y r

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3-2 The component of vector Resolve or decompose vector on the x and y axis θ Hypotenuse (H) Opposite (O) Adjacent (A) θ x y r rxrx ryry

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I Quadrant x +, y+ sin +, cos +, tan + 0<<90 0 II x -, y+ sin +, cos -, tan <<180 0 III x -, y- sin -, cos -, tan <<270 0 IV x +, y - sin -, cos +, tan << α α360 0 –α or -α α

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O=? Ex1. O=?, H=? A O O=?, A=? Θ=? 2 1 θ=?, O=?

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Ex2. Say you walk 3 m right and 11 m north, find the magnitude and direction of displacement. Ex3 θ O x y -2m -1 m r=?, θ=?

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3-2 Adding and Subtracting Vectors Adding vectors Graphically Connect vector head and tail, the sum vector is free tail to point free head A B C A B C D

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Adding Vectors: parallelogram method Adding Vectors Using Component C x =A x +B x C y =A y +B y Ex1. A=3, 20 0 ; B=5, 45 0 C=? A B C

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Ex2. C=? Ex3. A=2 m, θ=25 0; B=3 m, θ=60 0 Find | | and θ Ex4. A= 3 m, θ=60 0, B=5 m, θ= A B

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Subtracting Vectors D x =A x -B x D y =A x -B y Ex4. A= 10 m, 30 0 ; B=5 m, 60 0 Find, magnitude and direction ?

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