Impending motion on an incline: Compare the plane’s inclination with the angle of friction for motion to start. Condition: A block rests on a rough plane; angle of friction = φ; plane inclination = θ. Choose when the body will begin to move down the plane.

Given data

• Angle of friction φ where tanφ = μ (μ = coefficient of friction).
• Plane inclination θ.

Concept/Approach Limiting equilibrium down the plane occurs when tanθ = μ ⇒ θ = φ. Beyond this, friction cannot balance the component of weight down the plane and motion starts.

Step-by-step reasoning If θ < φ ⇒ tanθ < μ ⇒ at rest. If θ = φ ⇒ limiting equilibrium (on the verge of motion). If θ > φ ⇒ sliding commences.

Common pitfall Saying motion begins at θ = φ — that is only the brink. Actual motion requires θ > φ (assuming a nudge to overcome stiction).

Final Answer When θ is greater than φ