Key Concepts: Normal Force & Inclined Planes

Normal Force

• The normal force (N) is the perpendicular contact force a surface exerts on an object.
• On a flat surface: N = mg (weight). On an incline: N = mg cos θ.
• The normal force adjusts to prevent objects from passing through surfaces.

Inclined Planes

• Decompose weight into two components: parallel (mg sin θ, down the slope) and perpendicular (mg cos θ, into the surface).
• Without friction, acceleration down the slope = g sin θ.
• With friction: a = g sin θ − μₖg cos θ (down the slope).

Key Angles

• The angle of repose is the steepest angle at which an object stays stationary: tan θ = μₛ.
• At steeper angles, the object slides; at shallower angles, static friction holds it.