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{section:id=bigsection} {column:width=25%} {live-template:Left Column} {column} {column:width=75%} h2. Description and Assumptions {excerpt:hidden=true}*System:* Any. --- *Interactions:* Any. --- *Note:* Linear momentum evolves separately from angular momentum, so all system constituents are treated as [point particles] in this model.{excerpt} This model is [generally applicable|generally applicable model] (assuming knowledge of the external forces and system constituents). h2. Problem Cues This model is especially useful when describing the momentum of systems where external forces are absent (system momentum will be constant) or estimating the force in a process that occurs in a very short time interval as in collisions (impulse will be easier to determine than force). || Page Contents || | {toc:style=none|indent=10px|maxLevel=4} | ---- h2. Prerequisite Knowledge h3. Prior Models * [Point Particle Dynamics] h3. Vocabulary * [system] * [force] * [impulse] * [momentum] * [velocity] ---- h2. Compatible Systems The system must be effectively composed of [point particles|point particle], though rigid bodies may be treated as point particles with positions specified by the center of mass positions of the rigid body when this model is used. ---- h2. Relevant Interactions Only [external forces|external force] need be considered, since [internal forces|internal force] do not change the system's momentum. ---- h2. Model h3. Relevant Definitions \\ {latex}\begin{large}\[ \vec{p} = m\vec{v}\]\end{large}{latex} h3. Laws of Change | |
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| Wiki Markup | {section:id=smallsection}{column} h5. Differential Form {latex}\begin{large}\[ \sum_{\rm system}\frac{d\vec{p}}{dt} = \sum_{\rm external} \vec{F}\]\end{large}{latex} |
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| Wiki Markup | {column}{column} h5. Integral Form {latex}\begin{large}\[ \sum_{\rm system}\vec{p}_{f} = \sum_{\rm system}\vec{p}_{i} + \sum_{\rm external} \vec{J} = \sum_{\rm system}\vec{p}_{i} + \int \sum_{\rm external} \vec{F}\:dt \] \end{large}{latex} |
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| Wiki Markup | {column}{section:smallsection} ---- h2. Diagrammatic Representations * [Free body diagram|free body diagram]. * [Initial-state final-state diagram]. ---- h2. Relevant Examples {contentbylabel:constant_momentum,momentum_force,impulse|showSpace=false|showLabels=true|excerpt=true|operator=OR|maxResults=50} ---- {search-box} \\ {column} {section:bigsection} {live-template:RELATE license} \\ |
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