Syllabus References: M0.6 (Trigonometric functions), M4.2 (Vector representations), M4.4 (Scale vector diagrams), M4.5 (Resolving vectors into orthogonal components).
A vector possesses magnitude, unit, and direction. Resolving a vector replaces a single force with two orthogonal components whose vector sum reconstructs the original vector:
F_x · F_y = |F_x||F_y| cos(90°) = 0
Because the projection of F_x along the y-axis is zero, orthogonal axes are decoupled. Equilibrium or acceleration along the horizontal plane has zero mathematical influence on vertical dynamics.
Never assume horizontal components take cosine. The choice between sine and cosine depends strictly on the measured angle:
Inclined Planes: The weight vector acts vertically downward. The angle between the weight vector and the normal to the slope equals the incline angle α.
Adjust force magnitude and orientation to verify orthogonal components in real time.
Vary the incline angle and block mass to observe why normal contact force changes with slope angle.
This timed 20-question paper assesses numerical calculation, trigonometric projection, and vector diagrams to the Cambridge OCR standard.
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