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Conservation of Angular Momentum (view source)
Revision as of 19:44, October 1, 2016
, 19:44, October 1, 2016Maths formatting and a couple of minor corrections
'''Conservation of angular momentum''', fundamental concept of physics along with the conservations of mass and energy, and defined as mass multiplied by velocity of an object. It further states that the amount of momentum remains constant unless changed through an action of external forces as described by [[Isaac Newton|Newton's]] [laws of motion].
'''Conservation of angular momentum''', fundamental concept of physics along with the conversations of mass and energy as well as [[momentum (physics)|linear momentum]]. It further states that the amount of angular momentum remains constant unless changed through an action of external forces as described by [[Isaac Newton|Newton's]] [laws of motion].
The angular momentum of a point mass about a point is defined as <math>\vec H = \vec r \times \vec p</math> where '''r''' is the position [[vector quantity|vector]] of the point mass with respect to the point of reference and '''p''' is the [[momentum|linear momentum]] vector of the point mass.
The angular momentum of a point mass about a point is defined as <math>\vec H = \vec r \times \vec p</math> where <math>\vec{r}</math> is the position [[vector quantity|vector]] of the point mass with respect to the point of reference and <math>\vec{p}</math> is the [[momentum (physics)|linear momentum]] vector of the point mass.
The principle of angular momentum can be applied to a system of particles by summing the angular momentum of each particle about the same point.
The principle of angular momentum can be applied to a system of particles by summing the angular momentum of each particle about the same point. This can be represented as:
<math>
\vec{H}_{sys} = \sum_i \vec{H}_i
</math>
where
:<math>\vec{H}_{sys}</math> is the total angular momentum of the system
:<math>\vec{H}_i</math> is the angular momentum of the i<sup>th</sup> particle
The [[derivative]] of angular momentum with respect to time is equal to the sum of the external moments (or torque <math>\vec {\tau}</math>) applied to the system. Differentiating angular momentum gives:
The [[derivative]] of angular momentum with respect to time is equal to the sum of the external moments (or torque <math>\vec {\tau}</math>) applied to the system. Differentiating angular momentum gives:
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