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| {{Introduction|Angular momentum}}
| | If you are hard-working, blue collar person thinking about starting your own business from the scratch and have only a touch to get, you might consider janitorial cleaning company business. If it is public premise every business requires immaculately washed once-in a while and sometimes in a day. <br><br>As soon as you choose to take up a janitorial cleaning business. Like several other business, there are lots of steps involved you must get in to account: <br><br>1. You must register and decide your company name. <br><br>2. Obtain the business registrations and licenses from your own Local County or city hall. <br><br>3. Set up charge <br><br>4. Revenue Potential <br><br>5. Discover additional information about [https://plus.google.com/+TechnicleanindustriesOrgJanitorial/about find out more] by navigating to our lovely wiki. Printing marketing supplies <br><br>If you"re intending to work from home, you have to consult the zoning tips overseeing your residential area to test whether beginning e-commerce from home is granted. <br><br>Doing the right things from the start will require your cleaning business to another level of success. <br><br>It"s crucial that you sit down and figure out what will be launch cost to build a janitorial cleaning company. Your start-up costs could be around $500 - $5000. You may also start on a part-time basis working at home with only a vehicle and minimal level of equipment. <br><br>Nevertheless, janitorial specialist advises you that you must have a minimum of $50000 as an initial investment to start ecommerce right. <br><br>Starting your janitorial cleaning business as a home based business can put you in a much better place allowing to.. to you. <br><br>1. Keep your expenses low before you succeed in establishing some records and customer base. <br><br>2. As part of your original business strategy provide lower costs. <br><br>3. For alternative interpretations, consider looking at: [http://411.ca/business/profile/13753975 discount commercial cleaning service]. Work flexible hours generally on the part-time basis <br><br>4. [https://plus.google.com/+TechnicleanindustriesOrgJanitorial/about Tour Office Cleaning Vancouver] contains supplementary information concerning why to think over it. Raise your hours of operation <br><br>When you create your identity as a fruitful janitor/janitorial cleaning service provider in your area and environments, you can rent or lease a space with sufficient parking and storage space to keep your equipment and supplies effectively and safely. <br><br>A business "mundane" and may lacks glamour, nevertheless the janitorial service industry indicates remarkable development over the past decade and many experts think that the prospect for the industry over the coming years is quite brilliant..Techniclean Industries Corp<br>Unit # 211-7184-120 Street, <br>Surrey, BC<br>V3W 0M6<br>(604) 265-5577<br>www.technicleanindustries.org<br>info@technicleanindustries.com<br><br>Here is more information regarding buy health insurance online - [http://smellyferry4184.yolasite.com simply click the next internet page], review our own web-page. |
| {{Merge to|Angular momentum|date=April 2013}}
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| {{Textbook|date=February 2012}}
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| [[File:BehoudImpulsmoment.ogv|thumb|A video demonstration of angular momentum]]In [[physics]], '''angular momentum''' is the rotational counterpart of [[momentum|linear momentum]]. A freely-rotating disk (like a [[Frisbee]] in flight or a [[tire]] rolling down a hill) has angular momentum.
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| It is a [[Euclidean vector|vector]] quantity, meaning it has both direction and magnitude. The [[Magnitude (vector)|magnitude]] ''L'' of an object's angular momentum is
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| :<math>L = rp \sin\theta = rmv \sin\theta \, ,</math>
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| where ''r'' is the object's distance from the center of rotation (like the axis of a wheel or the sun in the solar system), {{nowrap|''p'' {{=}} ''mv''}} is the magnitude of its linear momentum, and ''θ'' is the angle between its [[position vector]] and its momentum vector.
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| In the [[SI system]] of units, angular momentum is measured in kg.m<sup>2</sup>.s<sup>−1</sup>. In contrast, linear momentum is measured in units of kg.m.s<sup>−1</sup> so the two are not compatible and cannot be added.
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| The angular momentum of a symmetrical body, such as a spinning [[flywheel]], is the product of the body's [[moment of inertia]] and its [[angular velocity]].
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| To calculate the angular momentum of a rotating object (a rigid body like a wheel or a system of objects like the solar system), a point called the ''origin'' is chosen. For convenience, this is usually the axis of rotation (of a rigid body) or the [[center of mass]] (of a system). The distance from the origin to each part of the object is multiplied by the transverse component of the linear momentum of that part. The sum of these vector quantities is the object's angular momentum.
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| ==Examples==
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| The following two examples, which were also very important in the history of physics, are very typical as cases where angular momentum is involved: the fact that a spinning upright [[gyroscope]] will remain upright and [[Kepler's laws of planetary motion#Second law|Kepler's second law]], which is a case of conservation of angular momentum.
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| [[Image:gyroskop.jpg|256px|thumb|left|A gyroscope remaining upright due to its spinning motion]]
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| [[Image:Kepler-second-law.svg|256px|thumb|none|[[Kepler's laws of planetary motion#Second law|Kepler's second law.]] As a planet orbits the Sun equal areas are swept out in equal intervals of time.]]
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| {{Clear}}
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| == The properties of angular momentum ==
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| Comparing ''angular momentum'' and ''momentum'' brings the properties of angular momentum into focus.
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| {|border="1" cellpadding="10" cellspacing="0" valign="top"
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| !Angular momentum
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| !Momentum
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| |- valign="top"
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| |The angular momentum of an object is defined relative to a fixed point. (In the case of a gyroscope the [[center of mass]] is used as the fixed point, in the case of Kepler's second law the much heavier Sun is used as the fixed point.) The amount of angular momentum of an object with respect to a fixed point '''S''' is proportional to the object's [[moment of inertia]] <math>I = mr^2</math>, and to the [[angular velocity]] relative to the fixed point. Multiplying those three factors gives the angular momentum. In notation:
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| : <math>L = I \omega </math>
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| Where ''L'' is the sign for angular momentum, ''I'' is the moment of inertia, ''r'' is the distance to the fixed point '''S''', and ''ω'' is the [[angular velocity]].
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| |The amount of ''momentum'' of an object is proportional to the object's mass, and to the [[velocity]]. Multiplying those two factors gives the momentum. In notation:
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| : <math>p = mv </math>
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| where ''p'' is the sign for momentum.
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| |- valign="top"
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| |The direction of [[angular velocity]] is defined with the help of the [[right hand rule]]. The direction of angular momentum is the same as the direction of the angular velocity.
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| |The direction of momentum is the direction of the velocity.
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| |- valign="top"
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| |In the absence of a [[torque]] both the amount and the direction of the angular momentum will not change.
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| |In the absence of a force both the amount and direction of momentum will not change.
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| |- valign="top"
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| |When two objects with a particular angular moment relative to a common fixed point '''S''' interact they affect each other's angular momentum; in this interaction the total angular momentum is conserved. Example: [[Gravity assist|Gravitational slingshot]]
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| |When two objects interact (in a collision for example), they affect each other's momentum; in this interaction the total momentum is conserved.
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| |}
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| Illustrating the properties with the example of a [[flywheel]]: if two flywheels have the same mass, and they are spinning at the same angular velocity, but one flywheel has a larger diameter than the other, then the larger diameter flywheel has more angular momentum. With a larger diameter the flywheel's mass is further away from the axis of rotation. The further away from the axis of rotation, the larger the required [[torque]] to spin up or spin down the flywheel within a particular measure of time.
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| Likewise, the larger the mass the larger the required torque, and the larger the angular velocity the larger the required torque.
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| == Newton's derivation of the area law ==
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| [[Image:Newton area law derivation.gif|frame|right|Newton's derivation of the area law using geometric means.]]
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| Newton's geometric derivation of the area law from the laws of motion: as an object orbits the Sun it sweeps out equal areas in equal intervals of time.
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| <ref>[http://www.vikdhillon.staff.shef.ac.uk/teaching/phy105/celsphere/phy105_derivation.html Discussion using Newton's original diagram for angular momentum derivation], University of Sheffield, England.</ref>
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| <ref>Proof that [http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Gravity/SecondLawDerivation.html angular momentum is proportional to area swept out by orbiting body], Western Washington University, USA</ref> The picture is adapted from Newton's original diagram, the underlying mathematics is the same. | |
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| An object (not shown) is in orbit around the Sun (point '''S'''). The effect of the Sun's gravitational attraction is represented as a sequence of instantaneous [[Impulse (physics)|impulses]], always directed towards point '''S'''. In the limit of the time interval between the impulses approaching to zero the sequence of impulses approaches infinitely close to continuous gravitational attraction.
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| When the object is at point '''B''' it receives an impulse towards point '''S'''. Without that impulse the object would proceed to point '''c'''. The actual displacement '''BC''' follows from the rules for velocity composition; the displacement '''BC''' is the vector sum of the displacements '''BV''' and '''Bc'''. The triangles '''SBc''' and '''SBC''' have the same base and the same height, hence they have the same surface area.
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| At point '''C''' the object receives another impulse towards point '''S'''. Without that impulse the object would have proceeded to point '''d''' in an equal interval of time. The impulse towards point '''S''' makes the object proceed to point '''D'''.
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| The triangles '''SBc''', '''SBC''', '''SCd''', '''SCD''', '''SDe''', '''SDE''' all have the same surface area.
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| In the limit of the time intervals going to infinitisimally small the sequence of lines connecting the points '''B''', '''C''', '''D''', '''E''', etc. approaches infinitely close to the actual continuous trajectory.
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| Note that this derivation proves a more general law than Kepler's law of areas. This derivation shows that the area law applies for ''any'' central force, not just for gravity.
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| === The area law as a case of angular momentum conservation. ===
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| That angular momentum is proportional to area swept out can be understood as follows: in the case of triangle '''SBC''' the length '''SB''' is equal to ''r'', the distance to the fixed point. The length '''BC''' correlates with the [[angular velocity]] relative to point S. Multiplying the angular velocity ω with ''r'' gives the length '''BC'''. Hence the area is proportional to ''r''*''r''*''ω'', and angular momentum is proportional to <math>r^2\omega </math><br>
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| Angular momentum involves a squared form: <math>r^2</math>. This is why in a geometrical representation angular momentum is proportional to an ''area'' rather than to a ''length''.
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| === Importance in the Principia ===
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| In Newton's major work, the [[Philosophiae Naturalis Principia Mathematica]] the above derivation is presented in Book I, Proposition I, Theorem I. Having the area law derived from first principles made it possible for Newton to represent the passage of time geometrically, which greatly enhanced Newton's possibilities for computations and proofs.
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| == General concept of angular momentum ==
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| {{Main|Angular momentum}}
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| The above description of angular momentum was restricted to a specific class of cases: the cases where the fixed point lies in the plane of rotation. This can be thought of as a planar version of angular momentum, only two dimensions of space are considered.
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| More generally the fixed point can be placed outside the plane of rotation. In this generalized concept of angular momentum all three of the spatial dimensions are considered.
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| ==See also==
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| * [[List of physics concepts in primary and secondary education curricula]]
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| == References ==
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| <references /> | |
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| ==External links==
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| * {{cite web|last=Bowley|first=Roger|title=Angular Momentum|url=http://www.sixtysymbols.com/videos/angular.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]|year=2009}}
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| [[Category:Physical quantities]]
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| [[Category:Rotation]]
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| [[Category:Conservation laws]]
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| [[simple:Angular momentum]]
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If you are hard-working, blue collar person thinking about starting your own business from the scratch and have only a touch to get, you might consider janitorial cleaning company business. If it is public premise every business requires immaculately washed once-in a while and sometimes in a day.
As soon as you choose to take up a janitorial cleaning business. Like several other business, there are lots of steps involved you must get in to account:
1. You must register and decide your company name.
2. Obtain the business registrations and licenses from your own Local County or city hall.
3. Set up charge
4. Revenue Potential
5. Discover additional information about find out more by navigating to our lovely wiki. Printing marketing supplies
If you"re intending to work from home, you have to consult the zoning tips overseeing your residential area to test whether beginning e-commerce from home is granted.
Doing the right things from the start will require your cleaning business to another level of success.
It"s crucial that you sit down and figure out what will be launch cost to build a janitorial cleaning company. Your start-up costs could be around $500 - $5000. You may also start on a part-time basis working at home with only a vehicle and minimal level of equipment.
Nevertheless, janitorial specialist advises you that you must have a minimum of $50000 as an initial investment to start ecommerce right.
Starting your janitorial cleaning business as a home based business can put you in a much better place allowing to.. to you.
1. Keep your expenses low before you succeed in establishing some records and customer base.
2. As part of your original business strategy provide lower costs.
3. For alternative interpretations, consider looking at: discount commercial cleaning service. Work flexible hours generally on the part-time basis
4. Tour Office Cleaning Vancouver contains supplementary information concerning why to think over it. Raise your hours of operation
When you create your identity as a fruitful janitor/janitorial cleaning service provider in your area and environments, you can rent or lease a space with sufficient parking and storage space to keep your equipment and supplies effectively and safely.
A business "mundane" and may lacks glamour, nevertheless the janitorial service industry indicates remarkable development over the past decade and many experts think that the prospect for the industry over the coming years is quite brilliant..Techniclean Industries Corp
Unit # 211-7184-120 Street,
Surrey, BC
V3W 0M6
(604) 265-5577
www.technicleanindustries.org
info@technicleanindustries.com
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