View source for Angular Impulse

Claimed by Katherine Delgado.

Angular impulse represents the effect of a moment of force, or torque (<math display="inline">\tau</math>), acting on a system over a certain period of time (<math display="inline">\Delta t</math>). Angular impulse helps indicate the direction that the system will rotate in (clockwise or counterclockwise) since it is associated with change in velocity and acceleration.

==The Main Idea==

Angular impulse is the torque acting over some time interval, or the change in angular momentum. Angular momentum can be changed by an angular impulse. There is no common symbol for angular momentum like how <math display="inline">\vec{F}</math> is for force and <math display="inline">\vec{p}</math> is for momentum, and as a result it is almost always referred to as <math display="inline">\Delta\vec{L}</math>, since it is equal to the change in angular momentum <math display="inline">\vec{L}</math>, just like how linear impulse (<math display="inline">J</math>) is equal to the change in linear momentum, <math display="inline">\Delta\vec{p}</math>.

===A Mathematical Model===

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

<math>\Delta \vec{L} = \sum{(\vec{F}\times\vec{d})}⋅\Delta t = \sum{\vec{\tau}}⋅\Delta t</math>

The angular impulse is equal to the moment of inertia <math display="inline">I</math> times the change in angular velocity <math display="inline">\Delta\vec{\omega}</math>.

<math>\Delta \vec{L} = I\Delta\vec{\omega} = I\vec{\omega_f} - I\vec{\omega_i}</math>


==== Angular Momentum Principle ====
The angular momentum principle directly involves angular impulse as shown in the image below:
[[File:Netangularimpulse.png]]

Both sides are equal to the net angular impulse for a system.

==== Units ====
The units for angular impulse are the same as those for angular momentum: <math display="inline">kg⋅m^2/s</math>.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

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

===Simple===
===Middling===
===Difficult===

==Connectedness==
Angular impulse is present in so many things in daily life, from wheels turning on a bicycle to turning the steering wheel in a car and even a person just spinning around in place. Personally, I'm really interested in computers, desktop computers in particular. This topic relates to the turning of fans in my case, on my graphics card, and on my processor, so angular momentum is critical when it can mean a negative one would result in drastically lower fan speeds that would make a computer overheat or a postive one would result in an increase in fan speed which would likely result in the fans being really noisy and annoying.

As a Computer Science major, angular momentum relates to actual computers in the example I gave previously. Not only that, but in the branch of artificial intelligence, if robots are involved then angular impulse can be critical in their circular motion.

Angular impulse has numerous industrial applications, being critical in any rotating device, like cars (wheels, steering wheels), generators, and even in water/wind mills which can provide hydroelectric/wind power.

==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===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]


==References==
Chapter 11 of [https://books.google.com/books?id=Gz4HBgAAQBAJ&pg=PA544&lpg=PA544&dq=matter+and+interactions+4th+edition+torque&source=bl&ots=ShdH7G8bcV&sig=uEQbxhpX3-UqcQf4ilXjp2reG5s&hl=en&sa=X&ved=0ahUKEwin-JTU6MTJAhWDQCYKHUoLA00Q6AEIMjAD#v=onepage&q&f=false Matter & Interactions 4th Edition]<div></div>
[https://en.wikipedia.org/wiki/List_of_equations_in_classical_mechanics#Derived_dynamic_quantities List of Equations in Classical Mechanics]<div></div>
[http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-13.html Lesson 13 Angular Impulse]<div></div>