Inclined Planes — Splitting Gravity into mg sinθ and mg cosθ

Gravity never stops pointing straight down, but the moment a surface tilts, that single straight-down force has to get split into two pieces that actually matter for motion: one along the slope, one into it. This video sets up that split from scratch using the same component method from vector pulling problems, then shows why normal force on a ramp is mg cosθ, never plain mg, and why that one substitution decides whether the rest of the problem comes out right. Covered in this video: Setting up the tilted free body diagram: why the axes rotate with the ramp instead of staying flat Splitting mg into mg sinθ (down the slope) and mg cosθ (into the surface), with the triangle that shows exactly why sine goes where it goes Why normal force on an incline is mg cosθ, not mg, and what changes if something else pushes on the block too Deriving a = g sinθ for a frictionless incline, and noticing the mass cancels exactly the way it did in free fall A fully worked example: a block sliding down a known angle, solving for both acceleration and normal force Adding friction into the same diagram and showing where μ_k mg cosθ enters the equation The trap: using mg instead of mg cosθ inside the friction formula, the single most common incline mistake This is core to Standard 2.3 (Newton's Laws and Forces) and is the formula every incline-pulley system in the next session is built directly on top of. AUX — Free Physics Resources https://auxlearning.com