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'''Conservation of angular momentum''', fundamental concept of physics along with the conversations of mass and energy as well as [[momentum (physics)|linear momentum]], and defined as mass multiplied by velocity of an object. 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 '''conservation of angular momentum''' is a fundamental concept of physics along with other [[conservation law]]s such as those of energy and [[momentum (physics)|linear momentum]]. It states that the angular momentum of a system remains constant unless changed through an action of external [[force]]s.

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.

In [[Newtonian mechanics]], 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. This can be represented as:

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}</math> is the total angular momentum of the system

:<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^th particle

:<math>\vec{H}_i</math> is the angular momentum of the i^th 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:

<math>\vec {\tau} = \vec r \times \vec F + \vec{\dot{r}} \times p</math>

<math>\vec {\tau} = \vec r \times \vec F + \vec{\dot{r}} \times p</math>

For a constant radius, the second term is zero. Hence <math>\vec {\tau}= \vec r \times \vec F</math> From this, it can be concluded that in the absence of an external moment, angular momentum must be conserved.

For a constant [[radius]], the second term is zero. Hence <math>\vec {\tau}= \vec r \times \vec F</math> From this, it can be concluded that in the absence of an external moment, angular momentum must be conserved.

[[Category:Physics]]

[[Category:Physics]]

[[Category:Mechanics]]

[[Category:Mechanics]]