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{excerpt:hidden=true}*[System|system]:* Any number of [rigid bodies|rigid body] or [point particles|point particle] whose angular momentum is constrained to one dimension. --- *[Interactions|interaction]:* Any that respect the [one-dimensional angular momentum|angular momentum (one-dimensional)].{excerpt}
h1. One-Dimensional Angular Momentum and Torque
h4. {toggle-cloak:id=desc} Description and Assumptions
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1-D Angular Momentum and Torque is a subclass of the general [Angular Momentum and External Torque] model in which a system of rigid bodies is constrained to move only in a plane (usually taken to be the _xy_ plane) with each body's angular momentum therefore directed along an axis perpendicular to the plane (along the z-axis). Under these conditions, the angular momentum is a one-dimensional vector, and the directional subscript (z) is generally omitted.
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h4. {toggle-cloak:id=cues} Problem Cues
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Systems involving several rigid bodies that interact. The integral form of this model is used in essentially all problems involving a collision where at least one body can rotate (e.g. a person jumping onto a rotating merry-go-round, a rotating disk falling onto another rotating object) or that involve a changing moment of inertia (spinning skater pulling her arms into her body). The differential form is useful in situations that involve the acceleration of a _system_ that involves rotation and acceleration and for which the forces are well understood (a single object can be treated with the simpler [Single-Axis Rotation of a Rigid Body]). For example, it could be used to solve for the acceleration of a modified Atwood's machine which involves a massive pulley that accelerates.
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h4. {toggle-cloak:id=pri} Prior Models
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* [Momentum and External Force]
* [Point Particle Dynamics]
* [Single-Axis Rotation of a Rigid Body]is helpful, but not necessary
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h4. {toggle-cloak:id=vocab} Vocabulary and Procedures
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* [torque (one-dimensional)]
* [angular momentum (one-dimensional)]
* [moment of inertia]
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h2. Model
h4. {toggle-cloak:id=sys} {color:red} Compatible Systems {color}
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The [system] can be composed of any number of [rigid bodies|rigid body] and [point particles|point particle]. The system must either be constrained to move in such a way that the [angular momentum|angular momentum (one-dimensional)] will be one-dimensional, or else the symmetries of the situation ([system] plus [interactions|interaction]) must guarantee that the [angular momentum|angular momentum (one-dimensional)] will remain one dimensional.
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h4. {toggle-cloak:id=int} {color:red} Relevant Interactions {color}
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External interactions must be explicitly given as torques, or as forces with their point of application or [moment arm] about the chosen axis specified along with their magnitude and direction. (Internal interactions do not change the angular momentum of the system.)
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h4. {toggle-cloak:id=def} {color:red} Relevant Definitions {color}
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Angular momentum about axis _a_:
{latex}\begin{large}\[ L_{a} = I_{cm}\omega + m\vec{r}_{{\rm cm},a}\times \vec{v}_{{\rm cm}} \]\end{large}{latex}
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h4. {toggle-cloak:id=laws} {color:red} Laws of Change {color}
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h5. Differential Form
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