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Momentum (physics) (view source)
Revision as of 14:12, September 11, 2016
, 14:12, September 11, 2016Tidy up, corrected a few points
==Angular momentum==
==Angular momentum==
A rotating or orbiting body possesses angular momentum. Like linear momentum, angular momentum is a vector quantity and is conserved. An object's angular momentum changes only when a [[torque]] is applied to it.
A rotating or orbiting body possesses angular momentum. Like linear momentum, angular momentum is a vector quantity and is conserved. An object's angular momentum changes only when a [[torque]] is applied to it. It is defined as:
:<math>\vec{L} = \vec{r} \times \vec{p}</math>
Where
*<math>\vec{L}</math> is the angular momentum
*<math>\vec{p}</math> is the linear momentum
*<math>\vec{r}</math> is the [[displacement]] vector from the origin to the particle
In [[classical mechanics]], the magnitude of the angular momentum of a particle orbiting some origin (such as the [[earth]] orbiting the [[sun]]) is given by
:<math>L=mvr</math>
:<math>L=mvr</math>
where
where
*'''L''' is angular momentum
*<math> L </math> is the magnitude angular momentum
*'''m''' is the mass of the particle
*<math> m </math> is the mass of the particle
*'''v''' is the linear velocity of the particle
*<math> v </math> is the tangential [[velocity]] of the particle
*'''r''' is the distance from the particle to the origin
*<math> r </math> is the distance from the particle to the origin
The direction of the angular momentum vector points perpendicularly to the plane formed by the object's orbit, in accordance with the [[right hand rule]].
The direction of the angular momentum vector points perpendicularly to the plane formed by the object's orbit, in accordance with the [[right hand rule]].
In addition to orbital angular momentum, the earth has rotational angular momentum due to its spin. The equations for calculating rotational angular momentum depend on the object's [[moment of inertia]], and therefore the shape and density of the object.
In addition to orbital angular momentum, the earth has rotational angular momentum due to its spin. The equations for calculating rotational angular momentum depend on the object's [[moment of inertia]], therefore the shape and density of the object and can be given as:
:<math>\vec{L} = I \vec{ \omega}</math>
Where
*<math>\vec{\omega}</math> is the angular momentum
*<math> I </math> is the [[moment of inertia]]
*<math>\vec{\omega}</math> angular velocity of the body
=== Generalized momentum ===
=== Generalized momentum ===
The definition of momentum can be generalized in [[Lagrangian Dynamics|Lagrangian]] and [[Hamiltonian Dynamics|Hamiltonian]] dynamics, to
The definition of momentum can be generalized in [[Lagrangian Dynamics|Lagrangian]] and [[Hamiltonian Dynamics|Hamiltonian]] dynamics, to
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