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Limiting Angle of Friction Formula

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The Limiting Angle of Friction is defined as the angle which the resultant reaction (R) makes with the normal reaction (RN). Check FAQs

Φ = a \tan (\frac{F lf}{R n})

Φ - Limiting Angle of Friction?F_lf - Limit Force?R_n - Normal Reaction?

Limiting Angle of Friction Example

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Here is how the Limiting Angle of Friction equation looks like with Values.

Here is how the Limiting Angle of Friction equation looks like with Units.

Here is how the Limiting Angle of Friction equation looks like.

2 = a \tan (\frac{0.225}{6.4431})

2° = a \tan (\frac{0.225N}{6.4431N})

2 = a \tan (\frac{0.225}{6.4431})

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Limiting Angle of Friction Solution

Follow our step by step solution on how to calculate Limiting Angle of Friction?

FIRST Step Consider the formula

Φ = a \tan (\frac{F lf}{R n})

Next Step Substitute values of Variables

∴

Φ = a \tan (\frac{0.225N}{6.4431N})

Next Step Prepare to Evaluate

∴

Φ = a \tan (\frac{0.225}{6.4431})

Next Step Evaluate

∴

Φ = 0.0349068935348381rad

Next Step Convert to Output's Unit

∴

Φ = 2.0000176754591°

LAST Step Rounding Answer

∴

Φ = 2°

Limiting Angle of Friction Formula Elements

Variables

Functions

Limiting Angle of Friction

The Limiting Angle of Friction is defined as the angle which the resultant reaction (R) makes with the normal reaction (RN).

Symbol: Φ

Measurement: AngleUnit: °

Note: Value should be less than 90.

Formulas to find Limiting Angle of Friction

Limit Force

Limit Force is the friction generated when two surfaces come in contact with each other.

Symbol: F_lf

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Limit Force

Normal Reaction

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.

Symbol: R_n

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Normal Reaction

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.

Syntax: 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.

Syntax: atan(Number)

Other formulas in Angle Friction category

Go Angle of Repose

α r = a \tan (\frac{F lim}{R n})

Go Coefficient of Friction between Cylinder and Surface of Inclined Plane for Rolling without Slipping

μ = \frac{\tan (θ i)}{3}

Go Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Downward

η = \frac{\tan (α i - Φ)}{\tan (α i)}

Go Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward

η = \frac{\tan (α i)}{\tan (α i + Φ)}

How to Evaluate Limiting Angle of Friction?

Limiting Angle of Friction evaluator uses Limiting Angle of Friction = atan(Limit Force/Normal Reaction) to evaluate the Limiting Angle of Friction, Limiting Angle of Friction formula is defined as the angle at which the force of friction just exceeds the normal reaction, causing an object to move or slide, and is a critical concept in understanding the interaction between surfaces in contact. Limiting Angle of Friction is denoted by Φ symbol.

How to evaluate Limiting Angle of Friction using this online evaluator? To use this online evaluator for Limiting Angle of Friction, enter Limit Force (F_lf) & Normal Reaction (R_n) and hit the calculate button.

FAQs on Limiting Angle of Friction

What is the formula to find Limiting Angle of Friction?

The formula of Limiting Angle of Friction is expressed as Limiting Angle of Friction = atan(Limit Force/Normal Reaction). Here is an example- 123.0476 = atan(0.225/6.4431).

How to calculate Limiting Angle of Friction?

With Limit Force (F_lf) & Normal Reaction (R_n) we can find Limiting Angle of Friction using the formula - Limiting Angle of Friction = atan(Limit Force/Normal Reaction). This formula also uses Tangent (tan), Inverse Tan (atan) function(s).

Can the Limiting Angle of Friction be negative?

No, the Limiting Angle of Friction, measured in Angle cannot be negative.

Which unit is used to measure Limiting Angle of Friction?

Limiting Angle of Friction is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Limiting Angle of Friction can be measured.

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