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PHY 430 – Lecture 2. Scalars & Vectors. 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. - PowerPoint PPT Presentation
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PHY 430 – Lecture 2Scalars & Vectors
1
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
2
Addition of Vectors – Graphical Methods – 1 Dimension
3
Addition of Vectors- Graphical Method – 2 Dimensions
4
5
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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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