Key Equations

Scalars & Vectors — AQA A-Level Physics

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Resultant of two perpendicular vectors
$$R = \sqrt{a^2 + b^2}$$
  • Where:
    • $R$ = resultant magnitude
    • $a$ = first vector magnitude
    • $b$ = second vector magnitude (perpendicular)
Only valid when vectors are at 90 degrees.
Horizontal component of a vector
$$F_x = F \cos \theta$$
  • Where:
    • $F_x$ = horizontal component
    • $F$ = vector magnitude
    • $θ$ = angle to horizontal
Use when angle is measured from the horizontal.
Vertical component of a vector
$$F_y = F \sin \theta$$
  • Where:
    • $F_y$ = vertical component
    • $F$ = vector magnitude
    • $θ$ = angle to horizontal
Use when angle is measured from the horizontal.
Weight component parallel to slope
$$F_{\parallel} = W \sin \theta$$
  • Where:
    • $F_parallel$ = component parallel to slope (N)
    • $W$ = weight (N)
    • $θ$ = angle of incline
On an inclined plane, this component drives the object down the slope.
Weight component perpendicular to slope
$$F_{\perp} = W \cos \theta$$
  • Where:
    • $F_perp$ = component perpendicular to slope (N)
    • $W$ = weight (N)
    • $θ$ = angle of incline
Equals the normal reaction force if there is no motion perpendicular to slope.
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