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Understanding Scalars and Vectors in Physics

This lecture introduces the fundamental concepts of scalars and vectors as essential building blocks in physics. Scalars are quantities defined solely by their magnitudes, such as mass, time, and temperature. In contrast, vectors are defined by both magnitude and direction, illustrated by examples including displacement, velocity, and acceleration. The session covers graphical methods for vector addition and subtraction, component analysis, unit vectors in a 3-D Cartesian coordinate system, and key vector products, fostering a comprehensive understanding of these concepts through mathematics and applications.

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Understanding Scalars and Vectors in Physics

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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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