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h2. Description and Assumptions

{excerpt:hidden=true}*System:* One [rigid body] rotating and translating such that its angular momentum is constrained to one-dimension and its moment of inertia is constant. --- *Interactions:* Any that respect the one-dimensional angular momentum.{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.

h2. Problem Cues

This model is useful for a stationary object (the special case of _statics_).  In that case, both the linear acceleration _a_ and the angular acceleration α are zero, and there is the additional freedom that the axis 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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h2. Prerequisite Knowledge

h4. Prior Models
* [Point Particle Dynamics]

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

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h2. System

One [rigid body].

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h2. Interactions

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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h2. Model 

h4. Laws of Change

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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h2. Diagrammatic Representations

* [Force diagram|force diagram]

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h2. Relevant Examples

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