Angular Impulse

Claimed by Katherine Delgado.

Angular impulse represents the effect of a moment of force, or torque ([math]\displaystyle{ \tau }[/math]), acting on a system over a certain period of time ([math]\displaystyle{ \Delta t }[/math]). Angular impulse indicates the direction that the system will rotate in (clockwise or counterclockwise).

The Main Idea

Angular impulse is the torque acting over some time interval, or the change in angular momentum. If it is positive, it results in the system rotating in a counterclockwise direction. If it is negative, the system will rotate in a clockwise direction. There is no common symbol for angular momentum like how [math]\displaystyle{ \vec{F} }[/math] is for force and [math]\displaystyle{ \vec{p} }[/math] is for momentum, and as a result it is almost always referred to as [math]\displaystyle{ \Delta\vec{L} }[/math], since it is equal to the change in angular momentum ([math]\displaystyle{ \vec{L} }[/math]), just like how linear impulse ([math]\displaystyle{ J }[/math]) is equal to the change in linear momentum, [math]\displaystyle{ \Delta\vec{p} }[/math].

A Mathematical Model

The angular impulse is equal to the net cross product of a force vector, [math]\displaystyle{ \vec{F} }[/math], applied at a particular location a vector distance [math]\displaystyle{ \vec{d} }[/math] from a pivot point times a specified time interval [math]\displaystyle{ \Delta t }[/math]. This is also equal to the net torque [math]\displaystyle{ \sum{\vec{\tau}} }[/math] times a specified time interval [math]\displaystyle{ \Delta t }[/math].

[math]\displaystyle{ \Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}*\Delta t = \sum{\vec{\tau}}*\Delta t }[/math]

[math]\displaystyle{ \Delta L = I\Delta\omega = I\omega_f - I\omega_i }[/math]

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Connectedness

1. How is this topic connected to something that you are interested in?
2. How is it connected to your major?
3. Is there an interesting industrial application?

History

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

See also

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading

Books, Articles or other print media on this topic

External links

[1]

References

This section contains the the references you used while writing this page