Dynamics · Physics

Inclined Planes

The incline is where components become real: resolve forces, choose smart axes, and solve motion.

This topic includes

Subtopics to master

From FBDs on slopes to acceleration with friction—this is a core mechanics skill.

Setup
Forces on an Incline
Draw the FBD correctly: weight, normal, friction (if present), and any applied forces.
  • Weight direction always down
  • Normal perpendicular to surface
  • Friction parallel to surface
Start subtopicClean diagram first.
Components
Resolve Parallel and Perpendicular Components
Break mg into components: mg sinθ along the slope and mg cosθ into the slope (with chosen axes).
  • Axis aligned with incline
  • sin/cos placement
  • Common trig mistakes
Start subtopicCore technique.
Normal
Normal Force on an Incline
Typically N = mg cosθ if there’s no acceleration perpendicular to the plane.
  • When N = mg cosθ holds
  • When it doesn’t
  • Perpendicular equilibrium
Start subtopicDon’t assume blindly.
Motion
Motion Up and Down an Incline
Write ΣF along the incline to find acceleration and solve kinematics if needed.
  • Choose sign convention
  • ΣF∥ = m a∥
  • Connect to motion equations
Start subtopicFull pipeline.
With friction
Inclines with Friction
Friction direction depends on the tendency of motion; magnitude uses μN (kinetic) or ≤ μsN (static).
  • Static vs kinetic decision
  • Direction logic
  • Threshold problems
Start subtopicMost common exam twist.
Practice
Practice & Exercises
Work through incline problems from basic components to friction + multi-step motion.
  • Component/trig drills
  • Find N and friction
  • Acceleration up/down slope
  • Static threshold questions
  • Exam-style multi-step sets
Open practiceMake inclines automatic.