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Learning Goal

Part of: Motion in Two Dimensions — 2 of 5 chapter items

Vector Addition and Subtraction: Analytical Methods

5.2

"For a two-dimensional vector, a **component** is a piece of a vector that points in either the x- or y-direction. Every 2-d vector can be expressed as a sum of its x and y components." "To find the magnitude *A* and direction θ of a vector from its perpendicular components **A**_x and **A**_y, we use the following relationships: A = √(A_x² + A_y²), θ = tan⁻¹(A_y/A_x)." "Note that tan⁻¹(θ) gives an angle in the first quadrant if A_y/A_x > 0 and in the fourth quadrant if A_y/A_x < 0. If, in fact, both A_x and A_y are negative, or if A_x is negative and A_y positive, then θ, measured from the positive x direction, is tan⁻¹(θ) + 180°."

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"For a two-dimensional vector, a component is a piece of a vector that points in either the x- or y-direction. Every 2-d vector can be expressed as a sum of its x and y components."
"To find the magnitude A and direction θ of a vector from its perpendicular components A_x and A_y, we use the following relationships: A = √(A_x² + A_y²), θ = tan⁻¹(A_y/A_x)."
"Note that tan⁻¹(θ) gives an angle in the first quadrant if A_y/A_x > 0 and in the fourth quadrant if A_y/A_x < 0. If, in fact, both A_x and A_y are negative, or if A_x is negative and A_y positive, then θ, measured from the positive x direction, is tan⁻¹(θ) + 180°."

What you'll learn

  1. Define the x- and y-components of a two-dimensional vector
  2. Resolve a vector into components using A_x = A cos θ and A_y = A sin θ
  3. Reconstruct a vector's magnitude and direction from its components using A = √(A_x² + A_y²) and θ = tan⁻¹(A_y/A_x)
  4. Add and subtract vectors analytically using the four-step component procedure
  5. Apply the quadrant rule to interpret the inverse-tangent result correctly

Slides

Interactive presentations perfect for visual learners • In development

Slides

In development

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