Inelastic collision: Difference between revisions

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{{lead too long|date=September 2013}}
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{{Classical mechanics|cTopic=Fundamental concepts}}
[[Image:angulardisplacement1.jpg|300px|right|thumb|Rotation of a rigid object ''P'' about a fixed object about a fixed axis ''O''.]]
 
'''Angular displacement''' of a body is the [[angle]] in [[radian]]s ([[degree (angle)|degree]]s, [[turn (geometry)|revolutions]]) through which a point or line has been rotated in a specified sense about a specified [[rotation|axis]].
 
When an object rotates about its axis, the motion cannot simply be analyzed as a particle, since in circular motion it undergoes a changing velocity and acceleration at any time (''t'').  When dealing with the rotation of an object, it becomes simpler to consider the body itself rigid.  A body is generally considered rigid when the separations between all the particles remains constant throughout the objects motion, so for example parts of its mass are not flying off.  In a realistic sense, all things can be deformable, however this impact is minimal and negligible.  Thus the rotation of a rigid body over a fixed axis is referred to as [[rotational motion]].  
 
In the example illustrated to the right, a particle on object P at a fixed distance ''r'' from the origin, ''O'', rotating counterclockwise. It becomes important to then represent the position of particle P in terms of its polar coordinates (''r'', ''θ''). In this particular example, the value of ''θ'' is changing, while the value of the radius remains the same. (In rectangular coordinates (''x'', ''y'') both ''x'' and ''y'' vary with time). As the particle moves along the circle, it travels an [[Arc (geometry)|arc length]] ''s'', which becomes related to the angular position through the relationship:
 
:<math>
s=r\theta \,</math>
 
==Measurements of angular displacement==
Angular displacement may be measured in [[radian]]s or degrees. If using radians, it provides a very simple relationship between distance traveled around the circle and the distance ''r'' from the centre.  
 
:<math>\theta=\frac sr</math>
 
For example if an object rotates 360 degrees around a circle of radius ''r'', the angular displacement is given by the distance traveled around the circumference - which is 2π''r''
divided by the radius: <math>\theta= \frac{2\pi r}r</math> which easily simplifies to <math>\theta=2\pi</math>. Therefore 1 revolution is <math>2\pi</math> radians.
 
<!-- Image with unknown copyright status removed: [[Image:angulardisplacement2.jpg|250px|left|thumb|A particle that is rotating from point P to point Q along the acr of the circle. In the time that elapses, the change in time is equal to the final time minus the original time, and the radius travels an angle theta, or the original angle subtracted from the final angle.]] -->
 
When object travels from point P to point Q, as it does in the illustration to the left, over <math>\delta t</math> the radius of the circle goes around a change in angle. <math>\Delta \theta = \Delta \theta_2 - \Delta \theta_1 </math> which equals the '''Angular Displacement'''.
 
== Three dimensions ==
In three dimensions, angular displacement is an entity with a direction and a magnitude. The direction specifies the axis of rotation, which always exists by virtue of the [[Euler's rotation theorem]]; the magnitude specifies the rotation in [[radian]]s about that axis (using the [[right-hand rule]] to determine direction).
 
Despite having direction and magnitude, angular displacement is not a [[vector (geometry)|vector]] because it does not obey the [[commutative law]] for addition.<ref>{{cite book|last1=Kleppner|first1=Daniel|last2=Kolenkow|first2=Robert|title=An Introduction to Mechanics|publisher=McGraw-Hill|year=1973|pages=288–89}}</ref>
 
=== Matrix notation ===
Given that any frame in the space can be described by a rotation matrix, the displacement among them can also be described by a rotation matrix. Being <math>A_0</math> and <math>A_f</math> two matrices, the angular displacement matrix between them can be obtained as <math>dA =  A_f . A_0^{-1}</math>
 
== References ==
<references />
 
==See also==
*[[Second moment of area]]
*[[Linear elasticity]]
*[[Rotation_matrix#Infinitesimal_rotations|Infinitesimal rotation]]
*[[Angular distance]]
 
[[Category:Angle]]

Latest revision as of 01:20, 15 August 2014

Are you always having issues with your PC? Are we always shopping for methods to heighten PC performance? Next this is the post you're trying to find. Here we are going to discuss a few of the most asked issues with regards to having you PC serve you well; how may I make my computer faster for free? How to create my computer run faster?

Many of the reliable firms can provide a full cash back guarantee. This means which you have the opportunity to receive the funds back should you find the registry cleaning has not delivered what you expected.

System tray icon makes it simple to launch the system and displays "clean" status or the amount of mistakes in the last scan. The ability to obtain plus remove the Invalid class keys plus shell extensions is one of the key blessings of the program. That is not routine function for the different Registry Cleaners. Class keys and shell extensions that are not functioning may seriously slow down your computer. RegCure scans to locate invalid entries and delete them.

It is regular which the imm32.dll error is caused due to a mis-deletion activity. If you cannot find the imm32.dll anywhere on your computer, there is no doubt which it must be mis-deleted whenever uninstalling programs or additional unneeded files. Hence, we can straight deal it from additional programs or download it from a secure web and then place it on your computer.

When it comes to software, this really is the vital part because it is the one running the program plus alternative programs required inside your works. Always maintain the cleanliness of the program from obsolete data by getting a advantageous system mechanic. Protect it from a virus online by providing a workable virus security program. You must moreover have a monthly clean up by running your defragmenter system. This means it can enhance the performance of the computer plus for you to avoid any errors. If you think anything is wrong with the software, plus you don't learn how to fix it then refer to a technician.

The most probable cause of the trouble is the system issue - Registry Errors! That is the reason why folks who absolutely have more than 2 G RAM on their computers are still consistently bothered by the problem.

Across the top of the scan results display page we see the tabs... Registry, Junk Files, Privacy, Bad Active X, Performance, etc. Each of these tabs can show you the results of which area. The Junk Files are mostly temporary files such as internet information, pictures, web pages... And they are just taking up storage space.

There are numerous firms that provide the service of troubleshooting a PC each time we call them, all you must do is signal up with them and for a little fee, we could have your machine usually working well plus serve you better.

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