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19 Pages

### Lecture 3

Course: PHY 2048, Spring 2008
School: University of Florida
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Word Count: 283

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Vectors Scalar: Ch3: just a number mass (m) time (t) pressure (P) temperature (T) energy (E) ... Vector: magnitude + direction displacement r velocity v acceleration a force F momentum p ... Adding Vectors c = a +b b a c a c b To add vectors, you can slide them as you wish as long as you preserve their direction Adding Vectors: examples c = a +b a a b a=3 b=4 120 b a=2 b=2 NOTE: a b Need to...

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Vectors Scalar: Ch3: just a number mass (m) time (t) pressure (P) temperature (T) energy (E) ... Vector: magnitude + direction displacement r velocity v acceleration a force F momentum p ... Adding Vectors c = a +b b a c a c b To add vectors, you can slide them as you wish as long as you preserve their direction Adding Vectors: examples c = a +b a a b a=3 b=4 120 b a=2 b=2 NOTE: a b Need to add vectors with different magnitudes, directions! Vector Components y ax = a cos a y = a sin ay a ax x 2 2 a 2 = ax + a y a = ax + a y Components depend on your choice of the coordinate system You need to know: cos 0 = 1 sin 0 = 0 cos 30 = sin 30 = 3 2 cos x 0 360 = 2 radians sin x, cos x look like this: 1 2 1 cos 60 = 2 sin 2 x x (rad) 3 sin 60 = 2 cos 90 = 0 sin 90 = 1 sin (x y) = sin x cos y cos x sin y cos(x y)= cos x cos y sin x sin y ... etc. See Appendix E in HRW Unit Vectors y ay a ^ i ^ | i | =1 j | ^ | =1 ax x ^ j ^ a = ax i + a y ^ j Example: ^ v = (2, 4, -1) = 2i + 4 ^ - k j ^ Adding Vector using Components y c = a +b b a cx = ax + bx c y = a y + by sin = cy c x c = c +c 2 x 2 y Example y c = a +b a a = 2, b = 4, = 30 x b ^ j A : c = 5.73i + ^ Example Multiplying Vectors Scalar product (dot-product): a ib = ab cos = ax bx + a y by + az bz Vector product (cross-product): b c = a b c = ab sin a c (a , b )-plane, direction: use right hand rule Examples 1 ^ a =i ^ b = -i + 3 ^ j a b = -1 ^ a b = 3 k b 3 1 a
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