Angle of Repose Definition and Expression

Angle of repose is the minimum angle of inclination at which the body starts sliding down from a inclined plane.Friction is a force which opposes relative motion.When a body is on a inclined plane,its weight acts vertically downward direction.But the inclined plane is not in that vertical direction,rather it is making some angle with the vertical.Hence entire weight is not acting on the inclination and only a part is acting normal to the surface of contact.

We can resolve weight into components as it is a vector quantity.One component is along the inclined plane where as the other component is perpendicular to the inclined plane as shown. The SIN component of weight tries to pull the body down the inclined plane and against it automatically frictional force is generated.This frictional force opposes motion of the body down the plane.It self adjusts itself to the applied force and keeps the body in the state of rest.This can happen until frictional force reaches its maximum and the maximum frictional force is also called as limiting friction.

We shall apply a force more than limiting friction, to move the body.This downward force is the SIN component of weight and it can be increased by increasing the angle of inclination.At a particular angle of inclination,down ward force along the plane is equal to the maximum frictional force and the body starts sliding down the inclined plane.This particular angle of inclination at which the body is about to start sliding down is called angle of repose.

If the angle of inclination is less than angle of repose,static frictional force self adjusts itself to the applied force and the body on the inclined plane is in the state of rest.It will be keep happening until the angle reach the angle of repose.

Once if the angle of inclination is equal to angle of repose,the body is about to slide down and ready to move.At this instant,downward force along the incline is equal to limiting frictional force.

If the angle of inclination is higher than angle of repose, the downward force along the plane is more than limiting frictional force and body starts sliding down with a acceleration. We can calculate that acceleration using Newton laws of motion.