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h2. DescriptionKeys to Applicability
{table:align=right|cellspacing=0|cellpadding=1|border=1|frame=box|width=40%}{tr}{td:align=center|bgcolor=#F2F2F2}*[Model Hierarchy]*{td}{tr}{tr}{td}{pagetree:root=Model Hierarchy|reverse=true}{td}{tr}{table}
{excerpt}This model is applicable to a _single_ [rigid body] that is both rotating and translating in such a way that its angular momentum is a one-dimensional vector (usually taken to lie along the z-axis). It is a subclass of the [1-D Angular Momentum and Torque] model defined by the constraint that the system consists of only one rigid body which has a fixed mass and a fixed moment of inertia for rotations about its center of mass.{excerpt}
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h2. Assumed Knowledge

h4. Prior Models
* [Point Particle Dynamics]
* [Fixed Axis Rotation of a Rigid Body]

h4. Vocabulary
* [force]
* [free body diagram]
* [torque (one-dimensional)]

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h2. Model Specification

h4. System Structure

Internal Constituents:*[Constituents|system constitutent]:*  One [rigid body].
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Environment:
*[Interactions|interaction]:*   Forces must be specified not only by their magnitude and direction, but also by either their point of application or [moment arm] with respect to the center of mass of the rigid body.

h4. Descriptors

Object*[State Variables|state variable]:*  Mass (_m_), and [moment of inertia] about the center of mass (_I_~cm~).  Both mass and moment of inertia must be constant to apply this model.  The moment of inertia may not be explicitly given, but there must be sufficient information to calculate it (often the mass plus some parameters of the rigid body's shape such as radius, length, etc.).

State*[Interaction Variables:  None.

Interaction Variables:|interaction variable]:*  Acceleration of the center of mass (_a_~cm~), angular acceleration about the center of mass (α~cm~), external forces (_F_^ext^) and torques about the center of mass (τ~cm~). 

h2. Model Equations

h4. Mathematical LawsStatement of Interaction the Model

This model implies the *simultaneous* equations:

{latex}\begin{large}\[ \sum \vec{F}^{ext} = mam\vec{a}_{cm}\]
\[ \sum \tau_{cm} = I_{cm}\alpha_{cm}\]\end{large}{latex}

h4. Laws of Change

None.

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h2. Relevant Examples

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