Angle of Repose in Physics Concept and Proof
Understand the angle of repose in physics — a key concept in mechanics that describes the steepest angle at which a body on an incline remains at rest without sliding.
What Is the Angle of Repose?
The angle of repose is the maximum angle between the surface of a slope and the horizontal at which a body placed on the slope just begins to slide. At this angle, the component of gravitational force down the plane equals the maximum static frictional force.
Concept and Forces
When a body rests on an inclined plane with angle θ, the forces acting on it are:
- Weight (mg) acting vertically downward
- Normal reaction (R) perpendicular to the plane
- Frictional force (f) opposing motion
Proof / Derivation
For a body at the verge of sliding, frictional force f = maximum static friction = μR.
The component of weight parallel to the plane = mg sinθ
The normal reaction = mg cosθ
At the angle of repose (θ = θr):
μR = mg sinθr
μ mg cosθr = mg sinθr
∴ tan θr = μ
θr = tan⁻¹(μ)
The angle of repose depends on the nature of the surfaces in contact — rougher surfaces result in a larger angle.
Angle of Repose in Physics Concept and Proof
Keywords
angle of repose in physics, angle of repose definition, tanθr equals μ, static friction, inclined plane mechanics, Class 11 physics, Class 12 physics, NEB physics, SEE physics, CTEVT physics, friction concept, mechanics derivation, physics notes
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angle of repose, friction, inclined plane, physics theory, Class 11, Class 12, NEB, SEE, CTEVT, mechanics, static friction, exam question, physics notes, aklearningnepal, education,Angle of Repose in Physics Concept and Proof
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Angle of Repose in Physics Concept and Proof