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{excerpt:hidden=true}*[System|system]:* One [rigid body] rotating about a fixed axis or rotating and translating such that its angular momentum is constrained to one-dimension and its moment of inertia is constant. --- *[Interactions|interaction]:* Any that respect the [one-dimensional angular momentum|angular momentum (one-dimensional)].{excerpt}


h1. Single-Axis Rotation of a Rigid Body

h4. {toggle-cloak:id=desc} Description and Assumptions

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This model is applicable to a _single_ [rigid body|rigid body] that is rotating about a fixed axis or else both rotating and translating in such a way that its [angular momentum|angular momentum (one-dimensional)] 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.
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h4. {toggle-cloak:id=cues} Problem Cues

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This [model|model] is useful for a stationary object (the special case of _statics_).  In that case, both the linear [acceleration|acceleration] _a_ and the angular acceleration α are zero, and there is the additional freedom that the [axis|axis of rotation] can be placed at any point in the object.  For accelerating objects, the model is commonly used in cases where a single object is placed in a situation where the forces are well understood, such as a cylinder rolling down an inclined plane or a sphere rolling along level ground.  Often, the linear and angular accelerations will be related by the [rolling without slipping] condition.     
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h4. {toggle-cloak:id=pri}Prior Models

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* [Point Particle Dynamics]

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h4. {toggle-cloak:id=vocab} Vocabulary

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

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h2. Model

h4. {toggle-cloak:id=sys} {color:red}Compatible Systems{color}

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One [rigid body|rigid body].

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h4. {toggle-cloak:id=int} {color:red} Relevant Interactions {color}

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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.

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h4. {toggle-cloak:id=laws} {color:red} Laws of Change {color}

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This model implies the *simultaneous* equations:

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

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h4. {toggle-cloak:id=diag} {color:red} Diagrammatic Representations {color}

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h2. Relevant Examples



h4. {toggle-cloak:id=all} All Examples Using this Model

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