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Composition Setup
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System: Any number of rigid bodies or point particles whose angular momentum is constrained to lie along a certain axis. — Interactions: Any that respect the one-dimensional angular momentum.
Introduction to the Model
Description and Assumptions
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.
Learning Objectives
Students are assumed to understand this model who can:
Relevant Definitions 
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}
S.I.M. Structure of the Model
Compatible Systems 
The system can be composed of any number of rigid bodies and point particles. The system must either be constrained to move in such a way that the angular momentum will be one-dimensional, or else the symmetries of the situation (system plus interactions) must guarantee that the angular momentum will remain one dimensional.
Relevant Interactions 
External interactions must be explicitly given as torques, or as forces with their point of application or moment arm about a chosen axis of rotation specified along with their magnitude and direction.  (Internal interactions do not change the angular momentum of the system.)
Laws of Change
Mathematical Representation
 Section
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Differential Form

 Latex
\begin{large}\[ \sum_{\rm system}\frac{dL_{a}}{dt} = \sum_{\rm external} \tau_{a} \]\end{large}
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Integral Form

 Latex
\begin{large}\[ \sum_{\rm system}L_{a,f} = \sum_{\rm system}L_{a,i} + \int \:\sum_{\rm external} \tau_{a} \:dt \]\end{large}
where the last term is called the "angular impulse"
Diagrammatic Representations
Relevant Examples
 
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idcons
 Examples Involving Constant Angular Momentum
 
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idcons
 falsetruetrue50constant_angular_momentum 

 
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idrws
 Examples Involving Rolling without Slipping
 
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idrws
 falsetruetrueAND50angular_momentum,rolling_without_slipping falsetruetrueAND50constant_angular_momentum,rolling_without_slipping 

 
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idpar
 Examples Involving the Parallel Axis Theorem
 
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idpar
 falsetruetrueAND50angular_momentum,parallel_axis falsetruetrueAND50constant_angular_momentum,parallel_axis 

 
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idall
 All Examples Using this Model
 
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idall
 falsetruetrueOR50angular_momentum,constant_angular_momentum 


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