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Angle of friction and repose
Intermediate
On an incline, sliding starts when tanθ exceeds μ.
tanθ = μThe angle of repose is the steepest slope at which an object stays at rest: tanθ = μₛ. Beyond it the block slides. It tells you μ by tilting a plane.
A block starts sliding at 25°: μₛ = tan25° ≈ 0.47.
Mass doesn't affect the angle.
In more detail
The angle of repose is the steepest angle at which an object stays at rest on a surface without sliding. At this angle, the tangent of the angle equals the coefficient of static friction.
Real-world uses
- Sand and gravel piles settle at their angle of repose.
- Engineers design slopes and embankments with safe angles of repose.
- Engineers use the angle of repose to decide the slope of a sand heap or a gravel pile that will stay stable.
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Frequently asked questions
What is the angle of repose for dry sand?
Typically around 30 to 35 degrees, depending on the grains.
How does it relate to friction?
The tangent of the angle of repose equals the coefficient of static friction.
What is the angle of repose?
The steepest angle at which material stays in place. It is set by the coefficient of friction between the grains.
Related topics in Newton's Laws & Forces
Motion on an inclined plane · Static friction · Kinetic friction · Rolling friction · Friction on inclines with applied force · Block on block problems