Torque - Revision history

Vipul: /* Units and dimensions */

2010-01-20T19:58:29Z

Units and dimensions

← Older revision		Revision as of 19:58, 20 January 2010
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	==Units and dimensions==		==Units and dimensions==

	~~The~~ dimensions ~~of torque are~~ <math>ML^2T^{-2}</math>~~, which are the same as those of energy. We can take the~~ units ~~to be~~ <math>J</math> (Joules) ~~though it is more customary to take the units as <math>J/rad</math> (Joules per radian).~~		{\| class="sortable" border="1"
			! Question !! Answer
			\|-
			\| Scalar or vector? \|\| [[Quantity type::Vector]]
			\|-
			\| Instantaneous or time-cumulative? \|\| [[Quantity type::Instantaneous]]
			\|-
			\| MLT dimensions \|\| <math>ML^2T^{-2}</math>: [[MLT::MLT;1;2;-2]]
			\|-
			\| SI units \|\| <math>J</math> (Joules)
			\|}

Vipul: /* Units and dimensions */

2010-01-19T23:58:02Z

Units and dimensions

← Older revision		Revision as of 23:58, 19 January 2010
Line 39:		Line 39:
	==Units and dimensions==		==Units and dimensions==

	The dimensions of torque are		The dimensions of torque are <math>ML^2T^{-2}</math>, which are the same as those of energy. We can take the units to be <math>J</math> (Joules) though it is more customary to take the units as <math>J/rad</math> (Joules per radian).

Vipul at 23:56, 19 January 2010

2010-01-19T23:56:48Z

← Older revision		Revision as of 23:56, 19 January 2010
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	==Definition==		==Definition==

	===Due to a single force===		===Due to a single force, about a point===

	Suppose <math>\overline{F}</math> is a [[force]] and <math>\overline{r}</math> is the radial vector from a point <math>A</math> to the point of application of <math>\overline{F}</math>. The '''torque''' due to <math>\overline{F}</math> about <math>A</math> is defined as the cross product of <math>\overline{r}</math> and <math>\overline{F}</math>. In other words, it is defined as:		Suppose <math>\overline{F}</math> is a [[force]] and <math>\overline{r}</math> is the radial vector from a point <math>A</math> to the point of application of <math>\overline{F}</math>. The '''torque''' due to <math>\overline{F}</math> about <math>A</math> is defined as the cross product of <math>\overline{r}</math> and <math>\overline{F}</math>. In other words, it is defined as:
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	Note that the torque, as a vector quantity, depends only on the point <math>A</math>, the ''line of action'' of <math>\overline{F}</math>, and the magnitude of <math>\overline{F}</math>. Thus, two forces of the same magnitude with the same line of action (Even though they may act at different points) generate the same torque.		Note that the torque, as a vector quantity, depends only on the point <math>A</math>, the ''line of action'' of <math>\overline{F}</math>, and the magnitude of <math>\overline{F}</math>. Thus, two forces of the same magnitude with the same line of action (Even though they may act at different points) generate the same torque.

			===Due to a single force, about an axis===

			Suppose <math>\overline{F}</math> is a [[force]] and <math>\overline{r}</math> is the vector from (and perpendicular to) a line <math>\ell</math> to the point of application of <math>\overline{F}</math>. The '''torque''' due to <math>\overline{F}</math> about <math>A\ell</math> is defined as the cross product of <math>\overline{r}</math> and <math>\overline{F}</math>. In other words, it is defined as:

			<math>\overline{\tau} = \overline{r} \times \overline{F}</math>

			The torque is a vector quantity. (More properly, torque is an alternating 2-tensor, and is treated as a vector via a (non-canonical) identification of <math>\R^3</math> with the space of alternating 2-tensors on <math>\R^3</math>).

			The magnitude of torque is given by:

			<math>\tau = \|rF \sin \theta\|</math>

			where <math>\theta</math> is the angle between the radial vector and the force vector.

	===Due to multiple forces===		===Due to multiple forces===

Vipul: Created page with '{{angular analogue of|force}} ==Definition== ===Due to a single force=== Suppose $\overline{F}$ is a force and $\overline{r}$ is the radial vector fr…'

2010-01-19T23:52:47Z

Created page with '{{angular analogue of|force}} ==Definition== ===Due to a single force=== Suppose <math>\overline{F}</math> is a force and <math>\overline{r}</math> is the radial vector fr…'

New page

{{angular analogue of|force}}

==Definition==

===Due to a single force===

Suppose <math>\overline{F}</math> is a [[force]] and <math>\overline{r}</math> is the radial vector from a point <math>A</math> to the point of application of <math>\overline{F}</math>. The '''torque''' due to <math>\overline{F}</math> about <math>A</math> is defined as the cross product of <math>\overline{r}</math> and <math>\overline{F}</math>. In other words, it is defined as:

<math>\overline{\tau} = \overline{r} \times \overline{F}</math>

The torque is a vector quantity. (More properly, torque is an alternating 2-tensor, and is treated as a vector via a (non-canonical) identification of <math>\R^3</math> with the space of alternating 2-tensors on <math>\R^3</math>).

The magnitude of torque is given by:

<math>\tau = |rF \sin \theta|</math>

where <math>\theta</math> is the angle between the radial vector and the force vector.

Note that the torque, as a vector quantity, depends only on the point <math>A</math>, the ''line of action'' of <math>\overline{F}</math>, and the magnitude of <math>\overline{F}</math>. Thus, two forces of the same magnitude with the same line of action (Even though they may act at different points) generate the same torque.

===Due to multiple forces===

The torque doe to multiple forces is defined as the vector sum of the torques due to each of the forces. When there is a continuum of forces, it is defined as a suitable integral. {{fillin}}

==Units and dimensions==

The dimensions of torque are

Torque - Revision history

Vipul: /* Units and dimensions */

Vipul: /* Units and dimensions */

Vipul at 23:56, 19 January 2010

Vipul: Created page with '{{angular analogue of|force}} ==Definition== ===Due to a single force=== Suppose \overline{F} is a force and \overline{r} is the radial vector fr…'

Vipul: Created page with '{{angular analogue of|force}} ==Definition== ===Due to a single force=== Suppose $\overline{F}$ is a force and $\overline{r}$ is the radial vector fr…'