Angle of friction - Revision history

Vipul: /* Definition */

2011-09-05T13:39:24Z

Definition

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	where <math>\mu_s</math> is the [[limiting coefficient of static friction]].		where <math>\mu_s</math> is the [[limiting coefficient of static friction]].

	Here, <math>\arctan</math> is the [[calculus:arc tangent function\|arc tangent function]], i.e., <math>\arctan(\mu_s)</math> is the angle <math>\theta</math> such that <math>\tan \theta = \mu_s</math>.		Here, <math>\arctan</math> is the [[calculus:arc tangent function\|arc tangent function]], i.e., <math>\arctan(\mu_s)</math> is the acute angle <math>\theta</math> such that <math>\tan \theta = \mu_s</math>.

	[[File:Blockonincline.png\|thumb\|300px\|right\|The block, if placed gently at rest, starts slipping only if the angle <math>\theta</math> is greater than the angle of friction for the block-incline pair of surfaces.]]		[[File:Blockonincline.png\|thumb\|300px\|right\|The block, if placed gently at rest, starts slipping only if the angle <math>\theta</math> is greater than the angle of friction for the block-incline pair of surfaces.]]

Vipul: /* Definition */

2011-09-05T13:37:32Z

Definition

← Older revision		Revision as of 13:37, 5 September 2011
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	Given two surfaces, the '''angle of friction''' (sometimes also termed the '''angle of repose''', though that term has another meaning in a related context) between the two surfaces is defined numerically as:		Given two surfaces, the '''angle of friction''' (sometimes also termed the '''angle of repose''', though that term has another meaning in a related context) between the two surfaces is defined numerically as:

	<math>\! \theta = \~~tan^{-1}~~(\mu_s)</math>		<math>\! \theta = \arctan(\mu_s)</math>

	where <math>\mu_s</math> is the [[limiting coefficient of static friction]].		where <math>\mu_s</math> is the [[limiting coefficient of static friction]].

			Here, <math>\arctan</math> is the [[calculus:arc tangent function\|arc tangent function]], i.e., <math>\arctan(\mu_s)</math> is the angle <math>\theta</math> such that <math>\tan \theta = \mu_s</math>.

	[[File:Blockonincline.png\|thumb\|300px\|right\|The block, if placed gently at rest, starts slipping only if the angle <math>\theta</math> is greater than the angle of friction for the block-incline pair of surfaces.]]		[[File:Blockonincline.png\|thumb\|300px\|right\|The block, if placed gently at rest, starts slipping only if the angle <math>\theta</math> is greater than the angle of friction for the block-incline pair of surfaces.]]

Vipul: /* External links */

2010-09-16T23:16:28Z

External links

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	===Instructional video links===		===Instructional video links===

	* [http://ocw.mit.edu/~~OcwWeb~~/~~Physics~~/8-~~01Physics~~-~~IFall1999~~/~~VideoLectures~~/~~detail~~/~~embed08.htm~~ MIT OCW lecture on friction by Walter Lewin] does not explicitly introduce the term "angle of friction" but derives the expression for it and also demonstrates an experiment to calculate it (time interval: 02:24 -- 08:58; continue on for more)		* [http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/embed08/ MIT OCW lecture on friction by Walter Lewin] does not explicitly introduce the term "angle of friction" but derives the expression for it and also demonstrates an experiment to calculate it (time interval: 02:24 -- 08:58; continue on for more)

Vipul: /* External links */

2010-09-15T22:34:19Z

External links

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	===Instructional video links===		===Instructional video links===

	* [http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/embed08.htm MIT OCW lecture on friction by Walter Lewin] does not explicitly introduce the term "angle of ~~repose~~" but derives the expression for it and also demonstrates an experiment to calculate it (time interval: 02:24 -- 08:58; continue on for more)		* [http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/embed08.htm MIT OCW lecture on friction by Walter Lewin] does not explicitly introduce the term "angle of friction" but derives the expression for it and also demonstrates an experiment to calculate it (time interval: 02:24 -- 08:58; continue on for more)

Vipul: /* Definition */

2010-09-15T22:31:18Z

Definition

← Older revision		Revision as of 22:31, 15 September 2010
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	where <math>\mu_s</math> is the [[limiting coefficient of static friction]].		where <math>\mu_s</math> is the [[limiting coefficient of static friction]].

			[[File:Blockonincline.png\|thumb\|300px\|right\|The block, if placed gently at rest, starts slipping only if the angle <math>\theta</math> is greater than the angle of friction for the block-incline pair of surfaces.]]
	It can be defined in the following ways:		It can be defined in the following ways:

	# It is the angle <math>\theta</math> that a fixed inclined plane made up of one surface must make with the horizontal so that a body with the second surfaces placed on it just starts slipping. In other words, for any angle smaller than <math>\theta</math>, slipping does not begin on its own and for any angle larger than <math>\theta</math>, slipping begins on its own.		# It is the angle <math>\theta</math> that a fixed inclined plane made up of one surface must make with the horizontal so that a body with the second surfaces placed on it just starts slipping. In other words, for any angle smaller than <math>\theta</math>, slipping does not begin on its own and for any angle larger than <math>\theta</math>, slipping begins on its own. {{further\|[[sliding motion along an inclined plane]]}}
	# Consider a block placed on a fixed horizontal plane such that the surfaces of contact are the two desired surfaces. Then, <math>\theta</math> is the angle such that the force needed to pull the block in a particular horizontal direction is minimum if the block is pulled at an angle <math>\theta</math> with that horizontal direction.		# Consider a block placed on a fixed horizontal plane such that the surfaces of contact are the two desired surfaces. Then, <math>\theta</math> is the angle such that the force needed to pull the block in a particular horizontal direction is minimum if the block is pulled at an angle <math>\theta</math> with that horizontal direction.

Vipul: /* Range of values */

2010-09-15T22:27:56Z

Range of values

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	[[File:Commonfrictioncoefficientsandanglesoffriction.png\|500px]]		[[File:Commonfrictioncoefficientsandanglesoffriction.png\|500px]]
			[[File:Commonfrictioncoefficientsandanglesoffrictionindegrees.png\|500px]]

	==External links==		==External links==

Vipul: /* Definition */

2010-09-15T22:24:08Z

Definition

← Older revision		Revision as of 22:24, 15 September 2010
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	For more information about motion on an inclined plane, refer [[sliding motion along an inclined plane]].		For more information about motion on an inclined plane, refer [[sliding motion along an inclined plane]].

	[[File:Angleoffrictionintermsofcoefficient.png\|thumb\|500px\|left]]		[[File:Angleoffrictionintermsofcoefficient.png\|thumb\|500px\|left\|The angle of friction in radians, concentrating on the range of typical values of friction coefficient.]]
	[[File:Angleoffrictionintermsofcoefficientindegrees.png\|thumb\|500px\|right]]		[[File:Angleoffrictionintermsofcoefficientindegrees.png\|thumb\|500px\|right\|The angle of friction in degrees, concentrating on the range of typical values of friction coefficient.]]
	[[File:Angleoffrictionintermsofcoefficient2.png\|thumb\|500px\|left]]		[[File:Angleoffrictionintermsofcoefficient2.png\|thumb\|500px\|left\|The angle of friction in radians, with asymptotic behavior clear.]]
	[[File:Angleoffrictionintermsofcoefficientindegrees2.png\|thumb\|500px\|right]]		[[File:Angleoffrictionintermsofcoefficientindegrees2.png\|thumb\|500px\|right\|The angle of friction in degrees, with asymptotic behavior clear.]]

			==Properties==

			The angle of friction is a strictly increasing function of the limiting coefficient of static friction <math>\mu_s</math>, taking the value <math>0</math> for the case <math>\mu_s = 0</math> and approaching the value <math>\pi/2 = 90\,^\circ</math> as <math>\mu_s \to \infty</math>.

	==Range of values==		==Range of values==

Vipul at 22:17, 15 September 2010

2010-09-15T22:17:44Z

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	[[File:Angleoffrictionintermsofcoefficient.png\|thumb\|500px\|left]]		[[File:Angleoffrictionintermsofcoefficient.png\|thumb\|500px\|left]]
	[[File:Angleoffrictionintermsofcoefficient2.png\|thumb\|500px\|right]]		[[File:Angleoffrictionintermsofcoefficientindegrees.png\|thumb\|500px\|right]]
			[[File:Angleoffrictionintermsofcoefficient2.png\|thumb\|500px\|left]]
			[[File:Angleoffrictionintermsofcoefficientindegrees2.png\|thumb\|500px\|right]]

	==Range of values==		==Range of values==

Vipul at 22:10, 15 September 2010

2010-09-15T22:10:11Z

← Older revision		Revision as of 22:10, 15 September 2010
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	For more information about motion on an inclined plane, refer [[sliding motion along an inclined plane]].		For more information about motion on an inclined plane, refer [[sliding motion along an inclined plane]].

			[[File:Angleoffrictionintermsofcoefficient.png\|thumb\|500px\|left]]
			[[File:Angleoffrictionintermsofcoefficient2.png\|thumb\|500px\|right]]

	==Range of values==		==Range of values==

	{{#lst:table of friction coefficients\|table}}		{{#lst:table of friction coefficients\|table}}

			[[File:Commonfrictioncoefficientsandanglesoffriction.png\|500px]]
	==External links==		==External links==

Vipul at 21:49, 20 January 2010

2010-01-20T21:49:43Z

← Older revision		Revision as of 21:49, 20 January 2010
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	For more information about motion on an inclined plane, refer [[sliding motion along an inclined plane]].		For more information about motion on an inclined plane, refer [[sliding motion along an inclined plane]].

			==Range of values==

			{{#lst:table of friction coefficients\|table}}
	==External links==		==External links==