Predicting Change in multiple dimensions: Difference between revisions
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<math>\Delta \overrightarrow{p}</math> = <math>\overrightarrow{p}_{final}-\overrightarrow{p}_{initial}</math> = <math>m\overrightarrow{v}_{final}-m\overrightarrow{ | <math>\Delta \overrightarrow{p}</math> = <math>\overrightarrow{p}_{final}-\overrightarrow{p}_{initial}</math> = <math>m\overrightarrow{v}_{final}-m\overrightarrow{v}_{initial}</math> | ||
| Line 25: | Line 25: | ||
<math>\Delta p = F \Delta t\,</math> | <math>\Delta p = F \Delta t\,</math> | ||
====Relate by Velocity==== | |||
Given the velocity: | Given the velocity: | ||
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<math>\overrightarrow{p} </math> = <math> \left(v_x,v_y,v_z \right) * \mathbf{m} </math> | <math>\overrightarrow{p} </math> = <math> \left(v_x,v_y,v_z \right) * \mathbf{m} </math> | ||
= <math> \left(\mathbf{m} v_x,\mathbf{m} v_y,\mathbf{m} v_z \right) </math> | |||
====Relate by Force==== | |||
Given the force: | |||
<math>\overrightarrow{F} = \left(F_x,F_y,F_z \right) </math> | |||
===A Computational Model=== | ===A Computational Model=== | ||
Revision as of 19:41, 29 November 2015
This page discusses the use of momentum to predict change in multi-dimensions and examples of how it is used.
Claimed by rbose7
The Main Idea
Linear momentum, or translational momentum of an object is equal to the product of the mass and velocity of an object. A change in any of these properties is reflected in the momentum.
If the object(s) are in a closed system not affected by external forces the total momentum of the system cannot change.
We can apply these properties to all three dimensions and use momentum to predict the path an object will follow over time by observing the change in momentum.
A Mathematical Model
This change in momentum is shown by the formula:
[math]\displaystyle{ \Delta \overrightarrow{p} }[/math] = [math]\displaystyle{ \overrightarrow{p}_{final}-\overrightarrow{p}_{initial} }[/math] = [math]\displaystyle{ m\overrightarrow{v}_{final}-m\overrightarrow{v}_{initial} }[/math]
Or by relating it to force:
[math]\displaystyle{ \Delta p = F \Delta t\, }[/math]
Relate by Velocity
Given the velocity:
[math]\displaystyle{ \overrightarrow{v} = \left(v_x,v_y,v_z \right) }[/math]
For an object with mass [math]\displaystyle{ \mathbf{m} }[/math]
The object has a momentum of :
[math]\displaystyle{ \overrightarrow{p} }[/math] = [math]\displaystyle{ \overrightarrow{v} * \mathbf{m} }[/math]
or:
[math]\displaystyle{ \overrightarrow{p} }[/math] = [math]\displaystyle{ \left(v_x,v_y,v_z \right) * \mathbf{m} }[/math]
= [math]\displaystyle{ \left(\mathbf{m} v_x,\mathbf{m} v_y,\mathbf{m} v_z \right) }[/math]
Relate by Force
Given the force:
[math]\displaystyle{ \overrightarrow{F} = \left(F_x,F_y,F_z \right) }[/math]
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
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