13. Moments - Revision history

Ian at 13:08, 27 April 2011

2011-04-27T13:08:43Z

←Older revision		Revision as of 13:08, 27 April 2011
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	{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"		{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
	\| style="border-bottom:1px solid #797979" width="5px" \|		\| style="border-bottom:1px solid #797979" width="5px" \|
-	{{Selected tab\|[[13. Moments\|Theory]]}}	+	{{Selected tab\|[[13. Moments\|Theory]]}}
	{{Not selected tab\|[[13. Exercises\|Exercises]]}}		{{Not selected tab\|[[13. Exercises\|Exercises]]}}
		+	{{Not selected tab\|[[13. Video\|Video]]}}
	\| style="border-bottom:1px solid #797979" width="100%"\|		\| style="border-bottom:1px solid #797979" width="100%"\|
	\|}		\|}
-
-

	== '''Key Points''' ==		== '''Key Points''' ==

Ian at 10:58, 26 June 2010

2010-06-26T10:58:13Z

←Older revision		Revision as of 10:58, 26 June 2010
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	\| valign="top"\|Moment (Nm)		\| valign="top"\|Moment (Nm)
	\|-		\|-
-	\|5N at O	+	\|5N at <math>O</math>
	\| valign="top"\| <math>5\times 0=0</math>		\| valign="top"\| <math>5\times 0=0</math>
	\|-		\|-

Ian at 10:50, 26 June 2010

2010-06-26T10:50:06Z

←Older revision		Revision as of 10:50, 26 June 2010
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	The resultant moment about <math>O</math> is the sum of the moments about <math>O</math>.		The resultant moment about <math>O</math> is the sum of the moments about <math>O</math>.
		+

	'''[[Example 13.1]]'''		'''[[Example 13.1]]'''

	[[Image:ex13.1whole.GIF]]		[[Image:ex13.1whole.GIF]]
-

	'''[[Example 13.2]]'''		'''[[Example 13.2]]'''

Ian at 13:42, 8 March 2010

2010-03-08T13:42:45Z

←Older revision		Revision as of 13:42, 8 March 2010
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	== '''Key Points''' ==		== '''Key Points''' ==

-	The moment of ~~the~~ force about the point O is the product of the force and the perpendicular distance to the line of action of the force from O.	+	The moment of a force about the point <math>O</math> is the product of the force and the perpendicular distance to the line of action of the force from <math>O</math>.

	[[Image:T13.1.GIF]]		[[Image:T13.1.GIF]]
-
	<math>\text{Moment }=Fd</math>		<math>\text{Moment }=Fd</math>

	[[Image:T13.2.GIF]]		[[Image:T13.2.GIF]]
-
	<math>\text{Moment }=Fd\sin \theta </math>		<math>\text{Moment }=Fd\sin \theta </math>

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	Anti-clockwise moments are positive.		Anti-clockwise moments are positive.

-		+	The resultant moment about <math>O</math> is the sum of the moments about <math>O</math>.

	'''[[Example 13.1]]'''		'''[[Example 13.1]]'''

Ian at 10:29, 17 February 2010

2010-02-17T10:29:08Z

←Older revision		Revision as of 10:29, 17 February 2010
Line 9:		Line 9:


-	Key Points	+	== '''Key Points''' ==

	The moment of the force about the point O is the product of the force and the perpendicular distance to the line of action of the force from O.		The moment of the force about the point O is the product of the force and the perpendicular distance to the line of action of the force from O.
-
-

	[[Image:T13.1.GIF]]		[[Image:T13.1.GIF]]

	<math>\text{Moment }=Fd</math>		<math>\text{Moment }=Fd</math>
-

	[[Image:T13.2.GIF]]		[[Image:T13.2.GIF]]

	<math>\text{Moment }=Fd\sin \theta </math>		<math>\text{Moment }=Fd\sin \theta </math>
-

	Clockwise moments are negative.		Clockwise moments are negative.
		+
	Anti-clockwise moments are positive.		Anti-clockwise moments are positive.

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	[[Image:ex13.1whole.GIF]]		[[Image:ex13.1whole.GIF]]
-
-
-


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	For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.		For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.
-

	[[Image:ex13.3.GIF]]		[[Image:ex13.3.GIF]]
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	{\| width="100%" cellspacing="10px" align="center"		{\| width="100%" cellspacing="10px" align="center"
	\|align="left"\| Force		\|align="left"\| Force
-	\| valign="top"\|Moment	+	\| valign="top"\|Moment (Nm)
	\|-		\|-
	\|5N at O		\|5N at O
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	\|valign="top"\| <math>-8\times 1\textrm{.}2=-9\textrm{.}6</math>		\|valign="top"\| <math>-8\times 1\textrm{.}2=-9\textrm{.}6</math>
	\|-		\|-
-
-
-
	\|7 N		\|7 N
	\| valign="top"\| <math>7\times 0=0</math>		\| valign="top"\| <math>7\times 0=0</math>

Ian at 09:39, 23 September 2009

2009-09-23T09:39:45Z

←Older revision		Revision as of 09:39, 23 September 2009
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	\|-		\|-
	\|8 N		\|8 N
-	\|valign="top"\| <math>-8\times 1.2=-9.6</math>	+	\|valign="top"\| <math>-8\times 1\textrm{.}2=-9\textrm{.}6</math>
	\|-		\|-

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	\|-		\|-
	\|6 N		\|6 N
-	\| valign="top"\| <math>-6\times 0.5=-3</math>	+	\| valign="top"\| <math>-6\times 0\textrm{.}5=-3</math>
	\|-		\|-
	\|5 N		\|5 N
-	\| valign="top"\| <math>5\times 1.2=6</math>	+	\| valign="top"\| <math>5\times 1\textrm{.}2=6</math>
	\|-		\|-
	\|4 N		\|4 N
-	\| valign="top"\| <math>4\times 0.5=2</math>	+	\| valign="top"\| <math>4\times 0\textrm{.}5=2</math>
	\|-		\|-
	\|Total Moment		\|Total Moment
-	\| valign="top"\| <math>0-9.6+0-3+6+2=-4.6\text{ Nm}</math>	+	\| valign="top"\| <math>0-9\textrm{.}6+0-3+6+2=-4\textrm{.}6\text{ Nm}</math>

	\|}		\|}

Ian at 11:14, 18 September 2009

2009-09-18T11:14:42Z

←Older revision		Revision as of 11:14, 18 September 2009
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-	Example 13.1	+
		+	'''[[Example 13.1]]'''

	[[Image:ex13.1whole.GIF]]		[[Image:ex13.1whole.GIF]]
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-	Example 13.2	+	'''[[Example 13.2]]'''

	[[Image:ex13.2.GIF]]		[[Image:ex13.2.GIF]]

-	Example 13.3	+
		+	'''[[Example 13.3]]'''

	For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.		For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.
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	[[Image:ex13.3.GIF]]		[[Image:ex13.3.GIF]]

-	Solution	+	'''Solution'''

	{\| width="100%" cellspacing="10px" align="center"		{\| width="100%" cellspacing="10px" align="center"

Ian at 11:09, 18 September 2009

2009-09-18T11:09:55Z

←Older revision		Revision as of 11:09, 18 September 2009
Line 50:		Line 50:
	Solution		Solution

-	Force Moment	+	{\| width="100%" cellspacing="10px" align="center"
-	5N at O	+	\|align="left"\| Force
-	<math>5\times 0=0</math>	+	\| valign="top"\|Moment
		+	\|-
		+	\|5N at O
		+	\| valign="top"\| <math>5\times 0=0</math>
		+	\|-
		+	\|8 N
		+	\|valign="top"\| <math>-8\times 1.2=-9.6</math>
		+	\|-

-	8 N
-	<math>-8\times 1.2=-9.6</math>

-	7 N
-	<math>7\times 0=0</math>

-	6 N	+	\|7 N
-	<math>-6\times 0.5=-3</math>	+	\| valign="top"\| <math>7\times 0=0</math>
		+	\|-
		+	\|6 N
		+	\| valign="top"\| <math>-6\times 0.5=-3</math>
		+	\|-
		+	\|5 N
		+	\| valign="top"\| <math>5\times 1.2=6</math>
		+	\|-
		+	\|4 N
		+	\| valign="top"\| <math>4\times 0.5=2</math>
		+	\|-
		+	\|Total Moment
		+	\| valign="top"\| <math>0-9.6+0-3+6+2=-4.6\text{ Nm}</math>

-	~~5 N~~	+	\|}
-	~~<math>5\times 1.2=6</math>~~	+
-		+
-	~~4 N~~	+
-	~~<math>4\times 0.5=2</math>~~	+
-		+
-	~~Total Moment~~	+
-	~~<math>0-9.6+0-3+6+2=-4.6\text{ Nm~~}~~</math>~~	+

Ian at 19:22, 17 September 2009

2009-09-17T19:22:29Z

←Older revision		Revision as of 19:22, 17 September 2009
Line 33:		Line 33:
	[[Image:ex13.1whole.GIF]]		[[Image:ex13.1whole.GIF]]

-	Find the moment of each force shown below about the point O.


-	[[Image:ex13.1.GIF]]
-
-	Solution
-
-	(a)
-
-	<math>20\times 0.8=16</math>
-
-	Moment is -16 Nm
-
-
-	(b)
-
-	<math>12\times 1.2=14.4</math>
-
-	Moment is 14.4 Nm
-


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	[[Image:ex13.2.GIF]]		[[Image:ex13.2.GIF]]

-	~~Find the moment of each force shown below about the point O~~.	+	Example 13.3
-	~~(a) (b)~~	+

-
-
-
-
-
-	Solution
-	(a) (b)
-
-
-
-
-
-
-
-
-
-
-	<math>40\times 3\sin 60{}^\circ =104</math>
-
-	<math>100\times 2\sin 20{}^\circ =68.4</math>
-
-
-	Moment is 104 Nm (to 3 sf) Moment is 68.4 Nm (to 3 sf)
-
-	Example 13.3
	For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.		For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.


-		+	[[Image:ex13.3.GIF]]
-		+
-		+
-		+
-		+
-		+
-		+

	Solution		Solution

Ian at 19:09, 17 September 2009

2009-09-17T19:09:45Z

←Older revision		Revision as of 19:09, 17 September 2009
Line 15:		Line 15:


-	[[Image:T13.GIF]]	+	[[Image:T13.1.GIF]]

-	<math>\text{Moment }=Fd</math> ~~<math>\ \ \ \ \ \ \ \ \ \text{Moment }=Fd\sin \theta </math>~~	+	<math>\text{Moment }=Fd</math>


-	~~Clockwise moments are negative~~.	+	[[Image:T13.2.GIF]]
-	~~Anti-clockwise moments are positive~~.	+

		+	<math>\text{Moment }=Fd\sin \theta </math>

-	Example 11.1
-	Find the moment of each force shown below about the point O.
-
-	(a) (b)

		+	Clockwise moments are negative.
		+	Anti-clockwise moments are positive.


		+	Example 13.1

		+	[[Image:ex13.1whole.GIF]]

		+	Find the moment of each force shown below about the point O.


		+	[[Image:ex13.1.GIF]]

	Solution		Solution
-	(a) ~~(b)~~	+
		+	(a)

	<math>20\times 0.8=16</math>		<math>20\times 0.8=16</math>
-
-	<math>12\times 1.2=14.4</math>

		+	Moment is -16 Nm

-	~~Moment is -16 Nm~~ Moment is 14.4 Nm	+
		+	(b)
		+
		+	<math>12\times 1.2=14.4</math>
		+
		+	Moment is 14.4 Nm

		+
		+
	Example 13.2		Example 13.2
		+
		+	[[Image:ex13.2.GIF]]
		+
	Find the moment of each force shown below about the point O.		Find the moment of each force shown below about the point O.
	(a) (b)		(a) (b)

←Older revision		Revision as of 13:08, 27 April 2011
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	{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"		{\| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
	\| style="border-bottom:1px solid #797979" width="5px" \|		\| style="border-bottom:1px solid #797979" width="5px" \|
-	{{Selected tab\|[[13. Moments\|Theory]]}}	+	{{Selected tab\|[[13. Moments\|Theory]]}}
	{{Not selected tab\|[[13. Exercises\|Exercises]]}}		{{Not selected tab\|[[13. Exercises\|Exercises]]}}
		+	{{Not selected tab\|[[13. Video\|Video]]}}
	\| style="border-bottom:1px solid #797979" width="100%"\|		\| style="border-bottom:1px solid #797979" width="100%"\|
	\|}		\|}
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	== '''Key Points''' ==		== '''Key Points''' ==