Angle of Repose Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angle of Repose = atan(Limiting Force/Normal Reaction)
αr = atan(Flim/Rn)
This formula uses 2 Functions, 3 Variables
Functions Used
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)
Variables Used
Angle of Repose - (Measured in Radian) - Angle of Repose is the angle that the plane of contact between two bodies makes with the horizontal when the upper body is just on the point of sliding.
Limiting Force - (Measured in Newton) - Limiting Force is the friction generated when two surfaces come in contact with each other.
Normal Reaction - (Measured in Newton) - The normal reaction is the force exerted by a surface on an object in contact with it which prevents the object from passing through the surface.
STEP 1: Convert Input(s) to Base Unit
Limiting Force: 5.125 Newton --> 5.125 Newton No Conversion Required
Normal Reaction: 6 Newton --> 6 Newton No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
αr = atan(Flim/Rn) --> atan(5.125/6)
Evaluating ... ...
αr = 0.706908060760116
STEP 3: Convert Result to Output's Unit
0.706908060760116 Radian -->40.5028483853398 Degree (Check conversion here)
FINAL ANSWER
40.5028483853398 40.50285 Degree <-- Angle of Repose
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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21 Angle Friction Calculators

Effort Applied to Move Body Downward on Inclined Plane Considering Friction
Go Effort to Move Downwards Considering Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction))/sin(Angle of Effort-(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction))
Effort Applied to Move Body Upward on Inclined Plane Considering Friction
Go Effort to Move Upwards Considering Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))/sin(Angle of Effort-(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))
Efficiency of Inclined Plane when Effort Applied to Move Body Downward
Go Efficiency of Inclined Plane = (cot(Angle of Inclination of Plane to Horizontal)-cot(Angle of Effort))/(cot(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)-cot(Angle of Effort))
Efficiency of Inclined Plane when Effort Applied to Move Body Upward
Go Efficiency of Inclined Plane = (cot(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)-cot(Angle of Effort))/(cot(Angle of Inclination of Plane to Horizontal)-cot(Angle of Effort))
Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward
Go Efficiency of Inclined Plane = sin(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)/(sin(Angle of Inclination of Plane to Horizontal)*cos(Limiting Angle of Friction))
Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Upward
Go Efficiency of Inclined Plane = (sin(Angle of Inclination of Plane to Horizontal)*cos(Limiting Angle of Friction))/sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
Effort Applied Parallel to Inclined Plane to Move Body Downward Considering Friction
Go Effort to Move Downwards Considering Friction = Weight of Body*(sin(Angle of Inclination of Plane to Horizontal)-Coefficient of Friction*cos(Angle of Inclination of Plane to Horizontal))
Effort Applied Parallel to Inclined Plane to Move Body Upward Considering Friction
Go Effort to Move Upwards Considering Friction = Weight of Body*(sin(Angle of Inclination of Plane to Horizontal)+Coefficient of Friction*cos(Angle of Inclination of Plane to Horizontal))
Effort Required to Move Body down Plane Neglecting Friction
Go Effort Required to Move Neglecting Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal))/sin(Angle of Effort-Angle of Inclination of Plane to Horizontal)
Effort Required to Move Body up Plane Neglecting Friction
Go Effort Required to Move Neglecting Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal))/sin(Angle of Effort-Angle of Inclination of Plane to Horizontal)
Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Downward
Go Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)/tan(Angle of Inclination of Plane to Horizontal)
Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward
Go Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal)/tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
Effort Applied Perpendicular to Inclined Plane to Move Body Downward Considering Friction
Go Effort to Move Downwards Considering Friction = Weight of Body*tan(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)
Effort Applied Perpendicular to Inclined Plane to Move Body Upward Considering Friction
Go Effort to Move Upwards Considering Friction = Weight of Body*tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
Frictional Force between Cylinder and Inclined Plane surface for Rolling without Slipping
Go Force of Friction = (Mass of Cylinder*Acceleration due to Gravity*sin(Angle of Inclination))/3
Effort Applied Perpendicular to Inclined Plane to Move Body along Inclination Neglecting Friction
Go Effort Required to Move Neglecting Friction = Weight of Body*tan(Angle of Inclination of Plane to Horizontal)
Effort Applied Parallel to Inclined Plane to Move Body Upward or Downward Neglecting Friction
Go Effort Required to Move Neglecting Friction = Weight of Body*sin(Angle of Inclination of Plane to Horizontal)
Limiting Angle of Friction
Go Limiting Angle of Friction = atan(Limit Force/Normal Reaction)
Angle of Repose
Go Angle of Repose = atan(Limiting Force/Normal Reaction)
Minimum Force Required to Slide Body on Rough Horizontal Plane
Go Minimum Effort = Weight of Body*sin(Angle of Effort)
Coefficient of Friction between Cylinder and Surface of Inclined Plane for Rolling without Slipping
Go Coefficient of Friction = (tan(Angle of Inclination))/3

Angle of Repose Formula

Angle of Repose = atan(Limiting Force/Normal Reaction)
αr = atan(Flim/Rn)

What is the difference between angle of friction and angle of repose?

Angle of Friction is the angle between the normal force (N) and the resultant force (R) of normal force and friction. Angle of Repose is the angle of maximum slope, where an object placed just begins to slide.

How to Calculate Angle of Repose?

Angle of Repose calculator uses Angle of Repose = atan(Limiting Force/Normal Reaction) to calculate the Angle of Repose, Angle of repose is the angle that the plane of contact between two bodies makes with the horizontal when the upper body is just on the point of sliding. Angle of Repose is denoted by αr symbol.

How to calculate Angle of Repose using this online calculator? To use this online calculator for Angle of Repose, enter Limiting Force (Flim) & Normal Reaction (Rn) and hit the calculate button. Here is how the Angle of Repose calculation can be explained with given input values -> 2320.642 = atan(5.125/6).

FAQ

What is Angle of Repose?
Angle of repose is the angle that the plane of contact between two bodies makes with the horizontal when the upper body is just on the point of sliding and is represented as αr = atan(Flim/Rn) or Angle of Repose = atan(Limiting Force/Normal Reaction). Limiting Force is the friction generated when two surfaces come in contact with each other & The normal reaction is the force exerted by a surface on an object in contact with it which prevents the object from passing through the surface.
How to calculate Angle of Repose?
Angle of repose is the angle that the plane of contact between two bodies makes with the horizontal when the upper body is just on the point of sliding is calculated using Angle of Repose = atan(Limiting Force/Normal Reaction). To calculate Angle of Repose, you need Limiting Force (Flim) & Normal Reaction (Rn). With our tool, you need to enter the respective value for Limiting Force & Normal Reaction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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