Angular Momentum Compared to Linear Momentum
claimed by jmcmahon9
The Main Idea
Linear momentum is great and all, but angular momentum is where the magic of physics kicks into high gear. See the transition of motion from translational to rotational calls for adding another variable that drastically changes the equations for linear motion that we know and love. The two that I will focus on are the equations for both angular and linear momentum.
Linear momentum is relatively simple, it depends upon the mass and velocity of an object, and to an extent the equation for angular momentum mimics the equation for linear momentum, but angular momentum draws a relationship between mass, velocity, AND the radius from the axis to the mass about which it is rotating. Now that your motion is relative to an axis, all of a sudden WHERE your mass is in relation to that axis MATTERS, and so the radius wriggles its way into the equations for linear motion, which makes these new equations have similar form but function in a completely different way.
A Mathematical Model
- Linear momentum: [math]\displaystyle{ \vec{p} = m*\vec{v} }[/math]
- Rotational angular momentum: [math]\displaystyle{ \vec{L}_{rot} = I*\vec{ω} }[/math]
- Translational angular momentum: <math? \vec{L}_{trans} = |\vec{r}|*|\vec{p}|sin{θ}
What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.
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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