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h2. Description {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. 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.{excerpt} ---- ||Page Contents|| |{toc:style=none|indent=10px}| ---- 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)] ---- h2. Model Specification h4. System Structure Internal Constituents:  One [rigid body]. \\ Environment:  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 Variables:  Mass (_m_), [moment of inertia] about the center of mass (_I_~cm~). 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 Variables:  None. Interaction Variables:  Acceleration of the center of mass (_a_~cm~), angular acceleration about the center of mass (α~cm~), forces (_F_) and torques about the center of mass (τ~cm~). h4. Laws of Interaction {latex}\begin{large}\[ \sum F = ma_{cm}\] \[ \sum \tau_{cm} = I_{cm}\alpha_{cm}\]\end{large}{latex} h4. Laws of Change None. ---- h2. Relevant Examples {contentbylabel:example_problem,rotation_translation,rotational_motion|showSpace=false|showLabels=true|excerpt=true|operator=AND|maxResults=50} ---- {search-box} \\ \\ | !copyright and waiver^copyrightnotice.png! | RELATE wiki by David E. Pritchard is licensed under a [Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License|http://creativecommons.org/licenses/by-nc-sa/3.0/us/]. | \\
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System: One rigid body rotating about a fixed axis or rotating and translating such that its angular momentum is constrained to one-dimension and the moment of inertia about its center of mass is constant. — Interactions: Any that respect the one-dimensional angular momentum.
Introduction to the Model
Description and Assumptions
This model is applicable to a single rigid body that is rotating about a fixed axis or else 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). As a special case, this model is also useful to constrain the forces acting on a static rigid body. It is a subclass of the Angular Momentum and External Torque about a Single Axis 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 the fixed axis or its center of mass.
Learning Objectives
Students will be assumed to understand this model who can:
S.I.M. Structure of the Model
Compatible Systems
One rigid body whose moment of inertia calculated about the chosen axis of rotation is constant.
Relevant Interactions
Only external torques need be considered, as internal torques do not produce angular accelerations. Since torque is needed, 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 axis of rotation. Allowed choices of the axis of rotation will depend upon the specific 
 circumstances of the problem:
Laws of Change
Mathematical Representation
 Latex
\begin{large} \[ \sum \tau_{a}^{\rm ext} = I_{a}\alpha\]\end{large}
Diagrammatic Representations
Relevant Examples
 
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idfix
 Examples Involving a Fixed Axis
 
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idfix
 falsetruetrueAND50example_problem,fixed_axis
 
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idtrans
 Examples Involving a Rotating and Translating Rigid Body
 
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idtrans
 falsetruetrueAND50rotation_translation,example_problem
 
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idstat
 Examples Involving a Static Rigid Body
 
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idstat
 falsetruetrueAND50example_problem,statics
 
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idall
 All Examples Using this Model
 
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idall
 falsetruetrueOR50rotation_translation,statics,fixed_axis


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 U.S. Navy by Mass Communications Specialist 3rd Class Walter M. Wayman
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