Force systems - Revision history

wikademia>Wikademia: Text replace - '[[Topic:' to '[['

2009-06-08T03:54:32Z

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	'''Part of the [[~~Topic:~~Statics\|Statics]] course offered by the ''[[~~Topic:~~Applied Mechanics\|Division of Applied Mechanics]]'', ''[[Engineering\|School of Engineering]]'' and the ''[[Portal:Engineering and Technology\|Engineering and Technology Portal]]'''''		'''Part of the [[Statics\|Statics]] course offered by the ''[[Applied Mechanics\|Division of Applied Mechanics]]'', ''[[Engineering\|School of Engineering]]'' and the ''[[Portal:Engineering and Technology\|Engineering and Technology Portal]]'''''

	==Lecture==		==Lecture==

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	'''Part of the [[Topic:Statics\|Statics]] course offered by the ''[[Topic:Applied Mechanics\|Division of Applied Mechanics]]'', ''[[~~School:~~Engineering\|School of Engineering]]'' and the ''[[Portal:Engineering and Technology\|Engineering and Technology Portal]]'''''		'''Part of the [[Topic:Statics\|Statics]] course offered by the ''[[Topic:Applied Mechanics\|Division of Applied Mechanics]]'', ''[[Engineering\|School of Engineering]]'' and the ''[[Portal:Engineering and Technology\|Engineering and Technology Portal]]'''''

	==Lecture==		==Lecture==

wikademia>Wikademia at 21:10, 11 April 2009

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	[[Category:Statics]]		[[Category:Statics]]
			{{ntnes}}

wikademia>Wikademia: Text replace - 'w:' to 'Wikipedia:'

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	===Force Vectors===		===Force Vectors===
	[[Image:Vector_components.png\|right\|200px\|thumb]]		[[Image:Vector_components.png\|right\|200px\|thumb]]
	A force vector is a force defined in two or more dimensions with a component vector in each dimension which may all be summed to equal the force vector. Similarly, the magnitude of each component vector, which is a scalar quantity, may be multiplied by the [[w:unit vector\|unit vector]] in that dimension to equal the component vector.		A force vector is a force defined in two or more dimensions with a component vector in each dimension which may all be summed to equal the force vector. Similarly, the magnitude of each component vector, which is a scalar quantity, may be multiplied by the [[Wikipedia:unit vector\|unit vector]] in that dimension to equal the component vector.

	<math>\vec F = \vec F_x + \vec F_y + \vec F_z = F_x\hat{i} + F_y\hat{j} + F_z\hat{k}</math>		<math>\vec F = \vec F_x + \vec F_y + \vec F_z = F_x\hat{i} + F_y\hat{j} + F_z\hat{k}</math>
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	===Moment===		===Moment===

	For a system wherein a rigid body experiences a force '''F''' at a orthogonal distance '''L''' from a fixed point, the ''moment'' '''M''' is the quantity (oddly enough of the same units as energy) defined by the force multiplied by the length of distance between the fixed point and the point where the force is applied. The direction of the moment is perpendicular to the force ecotro and the length, using the [[w:right hand rule\|right hand rule]].		For a system wherein a rigid body experiences a force '''F''' at a orthogonal distance '''L''' from a fixed point, the ''moment'' '''M''' is the quantity (oddly enough of the same units as energy) defined by the force multiplied by the length of distance between the fixed point and the point where the force is applied. The direction of the moment is perpendicular to the force ecotro and the length, using the [[Wikipedia:right hand rule\|right hand rule]].

	<math> \vec M \ = \vec F * L </math>		<math> \vec M \ = \vec F * L </math>
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	The general case in three dimensions can be calculated with the [[Vectors\|cross product]]. Do note that the order of the distance vector <math>\vec r</math> and the force <math>F</math> does matter in cross products as opposite order will change signs.		The general case in three dimensions can be calculated with the [[Vectors\|cross product]]. Do note that the order of the distance vector <math>\vec r</math> and the force <math>F</math> does matter in cross products as opposite order will change signs.
	<math> \vec M \ = \vec r \times \vec F </math>		<math> \vec M \ = \vec r \times \vec F </math>
	The components of a moment vector is the moment around the respective axis, following the [[w:right hand rule\|right hand rule]].		The components of a moment vector is the moment around the respective axis, following the [[Wikipedia:right hand rule\|right hand rule]].

	[[Image:Moment.PNG\|right\|350px\|thumb]]		[[Image:Moment.PNG\|right\|350px\|thumb]]
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	'''Study guide:'''		'''Study guide:'''
	# Wikipedia article:[[w:Force System\|Force System]]		# Wikipedia article:[[Wikipedia:Force System\|Force System]]
	# Wikipedia article:[[w:Vector\|Vector]]		# Wikipedia article:[[Wikipedia:Vector\|Vector]]
	# Wikipedia article:[[w:Force Vector\|Force Vector]]		# Wikipedia article:[[Wikipedia:Force Vector\|Force Vector]]
	# Wikipedia article:[[w:Moment\|Moment]]		# Wikipedia article:[[Wikipedia:Moment\|Moment]]
	# Wikipedia article:[[w:Couple\|Couple]]		# Wikipedia article:[[Wikipedia:Couple\|Couple]]
	# Wikipedia article:[[w:Resultant\|Resultant]]		# Wikipedia article:[[Wikipedia:Resultant\|Resultant]]

	[[Category:Statics]]		[[Category:Statics]]

wikademia>Wikademia: 33 revisions

2009-04-10T19:59:51Z

33 revisions

← Older revision	Revision as of 19:59, 10 April 2009
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wikademia>Mikael Öhman at 00:43, 12 February 2009

2009-02-12T00:43:00Z

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	A force vector is a force defined in two or more dimensions with a component vector in each dimension which may all be summed to equal the force vector. Similarly, the magnitude of each component vector, which is a scalar quantity, may be multiplied by the [[w:unit vector\|unit vector]] in that dimension to equal the component vector.		A force vector is a force defined in two or more dimensions with a component vector in each dimension which may all be summed to equal the force vector. Similarly, the magnitude of each component vector, which is a scalar quantity, may be multiplied by the [[w:unit vector\|unit vector]] in that dimension to equal the component vector.

	<math>\vec F~~(x,y,z)~~ = \vec F_x + \vec F_y + \vec F_z = F_x\hat{i} + F_y\hat{j} + F_z\hat{k}</math>		<math>\vec F = \vec F_x + \vec F_y + \vec F_z = F_x\hat{i} + F_y\hat{j} + F_z\hat{k}</math>

	~~<br~~>

	===Moment===		===Moment===

	For a system wherein a rigid body experiences a force '''F''' at a distance '''L''' from a fixed point, the ''moment'' '''M''' is the quantity (oddly enough of the same units as energy) defined by the force multiplied by the length of distance between the fixed point and the point where the force is applied. The direction of the moment is perpendicular to the force ecotro and the length, using the [[w:right hand rule\|right hand rule]].		For a system wherein a rigid body experiences a force '''F''' at a orthogonal distance '''L''' from a fixed point, the ''moment'' '''M''' is the quantity (oddly enough of the same units as energy) defined by the force multiplied by the length of distance between the fixed point and the point where the force is applied. The direction of the moment is perpendicular to the force ecotro and the length, using the [[w:right hand rule\|right hand rule]].


	<math> \vec M \ = \vec F * L </math>		<math> \vec M \ = \vec F * L </math>


	In the event that a force impacts the rigid body at an angle other than a right angle <math>\vec F = F\angle\alpha = F_x + F_y</math>, the moment is determined by the component of the force vector <math>\vec F</math> that is orthogonal to the length '''L'''.		In the event that a force impacts the rigid body at an angle other than a right angle <math>\vec F = F\angle\alpha = F_x + F_y</math>, the moment is determined by the component of the force vector <math>\vec F</math> that is orthogonal to the length '''L'''.

	<br>		The general case in three dimensions can be calculated with the [[Vectors\|cross product]]. Do note that the order of the distance vector <math>\vec r</math> and the force <math>F</math> does matter in cross products as opposite order will change signs.
			<math> \vec M \ = \vec r \times \vec F </math>
			The components of a moment vector is the moment around the respective axis, following the [[w:right hand rule\|right hand rule]].

	[[Image:Moment.PNG\|~~left~~\|350px\|thumb]]		[[Image:Moment.PNG\|right\|350px\|thumb]]
	'''Example:'''		'''Example:'''

	M = Force * Length = 100 Newtons * 10 Meters = 1,000 Newton-meters (N-m)		M = Force * Length = 100 Newtons * 10 Meters = 1,000 Newton-meters (N-m)


	'''Example:'''		'''Example:'''
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	(Hint: draw a free body diagram)		(Hint: draw a free body diagram)

	Then <math> \vec M = F(a+b) - ~~(Fa)~~</math>		Then <math> \vec M = F(a+b) - F a</math>

			In 3D the same rule applies, using that
			<math> \vec M = \vec r_1 \times \vec F_1 + \vec r_2 \times \vec F_2 = \vec r_1 \times \vec F_1 - \vec r_2 \times \vec F_1 = (\vec r_1 - \vec r_2) \times \vec F_1</math>
			which means that the moment will be the same around any point in the system.

	===Resultant===		===Resultant===

wikademia>Gustable at 01:26, 6 July 2008

2008-07-06T01:26:32Z

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	[[Category:Statics]]		[[Category:Statics]]
	~~[[Category:Advanced Classical Mechanics]]~~
	~~[[Category:Applied Mechanics]]~~
	~~[[Category:Mechanical Engineering]]~~
	~~[[Category:Engineering]]~~

wikademia>Remi: Force Systems moved to Force systems: naming conventions

2008-03-01T11:02:35Z

Force Systems moved to Force systems: naming conventions

← Older revision	Revision as of 11:02, 1 March 2008
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wikademia>Mu301: /* Assignments */ name

2008-01-08T03:19:29Z

Assignments: name

← Older revision		Revision as of 03:19, 8 January 2008
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	==Assignments==		==Assignments==
	'''Activities:'''		'''Activities:'''
	* Create an [[activity]]		* Create an [[Force Systems/activity\|activity]]

	'''Readings:'''		'''Readings:'''

wikademia>Gustable: /* Moment */

2007-10-20T03:26:17Z

Moment

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	<br>		<br>

	[[Image:Moment.PNG\|left\|~~400px~~\|thumb]]		[[Image:Moment.PNG\|left\|350px\|thumb]]
	'''Example:'''		'''Example:'''