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Lecture 1

  1. Dimensional Analysis: Know the dimensions of basic quantities: Length (L), Time (T), Mass (M), Velocity (L/T), Acceleration (L/T²). Be ready to check if an equation is dimensionally consistent.
  2. Vector Decomposition (2D):
    • A_x = A cos(θ)
    • A_y = A sin(θ)
  3. Vector Representation:
    • A = A_x î + A_y ĵ + A_z k̂
  4. Vector Magnitude:
    • A = sqrt(A_x² + A_y² + A_z²)
  5. Vector Addition:
    • R_x = A_x + B_x
    • R_y = A_y + B_y
  6. The Dot Product:
    • Definition: A ⋅ B = A B cos(θ)
    • Calculation: A ⋅ B = A_x B_x + A_y B_y + A_z B_z
    • Key Property: A ⋅ B = 0 if the vectors are perpendicular.
  7. The Cross Product:
    • Magnitude: |***A*** × ***B***| = A B sin(θ)
    • Direction: Use the Right-Hand Rule.
    • Calculation: Use the Determinant Method.
    • Key Property: A × B is perpendicular to both A and B.

That concludes our first lecture. You've learned the fundamental mathematical language of physics. Do you have any final questions on any of these topics before we wrap up?