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Physics vectors post lecture

# Physics vectors post lecture - Physics 101 Lecture 4a...

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1 PHYS 101 - Lecture 4a 1 Physics 101 – Lecture 4a Vectors & Reference Frames Kinematics in 2- and 3-dimensions will require us to work with vectors . A “vector” is simply an array of numbers. Just as you’re used to specifying a position (or displacement!): x=5, y=10 as (5, 10) vector notation for velocity (or acceleration) is a shorthand way of specifying components of that velocity: v = (17.0, 3.2) m/s means: v x = 17.0 m/s, v y = 3.2 m/s PHYS 101 - Lecture 4a 2 We’ve noted that displacement, velocity and acceleration are vectors. In 1-D situations treated up to now, “vector” simply meant that a sign was necessary to specify the direction. For 2-D work we will have to deal with vector arithmetic : addition & subtraction of vector quantities. Two major approaches: graphical method & components method. Graphical method (really only works in 2-D): Add vectors using the “tip-to-tail” method: eg. a + b = c where a = b = Then = c a b

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2 PHYS 101 - Lecture 4a 3 Subtraction of a vector is the addition of its negative eg. a - b = c where a = b = Then The magnitude of the resulting vector is given by: |c| 2 = |a ± b| 2 = |a| 2 + |b| 2 ± 2ab cos(Θ) where Θ is the angle between a and b. Note this simplifies to Pythagoras’ theorem for Θ = 90 o : |c| 2 = |a + b| 2 = |a| 2 + |b| 2 a -b c = a - b Θ PHYS 101 - Lecture 4a 4 Fun with vectors: which vector is A – 2B ?
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