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PHY 430 – Lecture 2

This lecture explores the fundamental concepts of scalars and vectors, essential in physics. Scalars are quantities with only magnitudes, such as mass and temperature, while vectors have both magnitudes and directions, exemplified by displacement and velocity. We will cover graphical and analytical methods for adding and subtracting vectors, defining vector components, and utilizing unit vectors in a 3-dimensional Cartesian coordinate system. Additionally, we’ll discuss vector products, including the dot and cross product, and their implications in physics.

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PHY 430 – Lecture 2

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  1. PHY 430 – Lecture 2 Scalars & Vectors

  2. 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

  3. Addition of Vectors – Graphical Methods – 1 Dimension

  4. Addition of Vectors- Graphical Method – 2 Dimensions

  5. Subtraction of Vectors

  6. Multiplication of a Vector by a Scalar

  7. Adding Vectors by Components – Resolving Vectors

  8. 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

  9. Resolving a vector = finding components of a vector

  10. Adding vectors analytically (by components)

  11. Unit Vectors

  12. 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

  13. Products of vectors • Dot product: A B =IAIIBIcos A  B = B  A • Cross Product: A X B =IAIIBIsin  n A x B = - B x A

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