PHY 430 – Lecture 2Scalars & Vectors

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3.1 Scalars & vectors

Scalars – quantities with only magnitudes Eg. Mass, time, temperature Mathematics - ordinary algebra

Vectors – quantities with magnitudes & directions Eg. Displacement, velocity, acceleration Mathematics - vector algebra

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Addition of Vectors – Graphical Methods – 1 Dimension

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Addition of Vectors- Graphical Method – 2 Dimensions

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Subtraction of Vectors

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Multiplication of a Vector by a Scalar

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Adding Vectors by Components – Resolving Vectors

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Two ways to specify a vector 1. Give its componens, Vx

and Vy

2. Give its magnitud V and angle it makes with positive x – axis

We can shift from one description to the other by using theorem of Pythagoras and definition of tangent

x

y

2y

2x

V

Vtan

VVV

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Resolving a vector = finding components of a vector

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Adding vectors analytically (by components)

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Unit Vectors

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Unit vectors

For 3-D Cartesian coordinate system i = unit vector in the direction of x j = unit vector in the direction of y k = unit vector in the direction of z Fig. 3-15

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Products of vectors

Dot product: A B = IAI IBI cos A B = B A

Cross Product: A X B = IAI IBI sin nA x B = - B x A

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