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	~~{{about\|the gyroscopic exercise tool~~ and ~~toy\|the US lottery\|Powerball\|other "powerballs"\|Powerball (disambiguation)}}~~		Friends call her Crissy Westfield and he or she totally digs that [http://search.un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=business&Submit=Go business]. For years I've been working like a filing assistant and it is something I enjoy. Her family lives in Idaho and her family loves this task. One of my favorite hobbies is greeting card collecting but I'm thinking on [http://en.search.wordpress.com/?q=starting starting] something state of the art. Check out his website here: http://www.acvglobal.com/dm/es/comprar-bolso-longchamp-online.html<br><br>Stop by my blog post ... [http://www.acvglobal.com/dm/es/comprar-bolso-longchamp-online.html Comprar Bolsos Longchamp Baratos]

	[~~[Image~~:~~Powerball neon green work~~.~~jpg\|thumb\|right\|Powerball Neon Green Pro – working]]~~

	~~A '''gyroscopic exercise tool''' is a device used to exercise the [[wrist]] as part of [[physical therapy]] or in order to build palm, forearm and finger strength~~. It can also be used as a unique demonstration of some aspects of [[dynamics (physics)\|rotational dynamics]]. The device consists of a [[tennis ball]]-sized plastic or metal shell around a free-spinning mass, which is started with a short rip string. Once the [[gyroscope]] inside is going fast enough, a person holding the device can accelerate the spinning mass to high revolution rates by moving the wrist in a circular motion.

	==~~Mechanics~~==
	~~{{Tone\|section\|date~~=~~June 2011}}~~
	~~[[Image:Gyrotwister.jpg\|thumb\|A DynaBee gyroscopic wrist exerciser.~~]]

	~~The device consists of a spinning mass inside an outer shell~~. ~~The shell almost completely covers the mass inside, with only~~ a small round opening allowing the gyroscope to be manually started. The spinning mass is fixed to a thin metal [[axle]], each end of which is trapped in a circular, equatorial groove in the outer shell. A lightweight ring with two notches in it for the ends of the axle rests in the groove. This ring can slip in the groove; it ~~holds the spinning gyroscope centered in the shell, preventing the two from coming into contact (which would slow the gyro down), but still allowing the orientation of the axle to change.~~

	~~Since the spinning mass~~ is ~~balanced, the only possibility to speed up the rotation is for the sides of the groove to exert forces on the ends of the axle~~. Furthermore, the normal and axial forces will have no effect, so tangential force must be provided by [[friction]]. If the axle is stationary, the friction will only act to slow down the rotation, but the situation is very different if the axle is turned by applying a [[torque]].

	~~This can be accomplished by tilting the shell in any direction except exactly~~ in ~~the plane of the groove,~~ and ~~results in a shift of the axle ends along the groove~~. The direction and speed of the shift can be found from the formula for the [[precession]] of a gyroscope: the applied torque is equal to the [[cross product]] of the [[angular velocity]] of precession and the [[angular momentum]] of ~~the spinning mass. The most important observation here~~ is ~~that the direction is such that, if the torque is large enough, the friction between the axle and the surface of the groove will speed up the rotation.~~

	This may seem odd. After all, if the axle were shifting in a horizontal groove, the friction on one end that acts to speed up the rotation would be canceled by the friction at the other end, operating in the opposite direction. The difference is that a torque is being applied, so one end of the axle is pushing against one side of the groove, while the other end is pushing against the other side. Likewise, it does not matter in which direction the torque is applied. If the torque is reversed, each end of the axle will then be pressing against the opposite side of the groove, but the direction of precession is also reversed. The only restriction is that the relative speed of the surface of the axle and the side of the groove due to precession, <math>\mathit{\Omega}_{\mathrm{P}} R_{\mathrm{groove}}</math>, must exceed the relative speed due to the rotation of the spinning mass, <math>\omega r_{\mathrm{axle}}</math>. The minimum torque required to meet this condition is <math> I ~~\omega^2 \left( r_{\mathrm{axle}} / R_{\mathrm{groove}} \right) </math>, where '''I''' is the [[moment of inertia]] of the spinning mass, and '''ω''~~' ~~is its angular velocity.~~

	Since an acceleration of the rotation will occur regardless of the direction of the applied torque, as long as it is large enough, the device will function without any fine-tuning of the driving motion. The tilting of the shell does not have to have a particular phase relationship with the precession or even to have the same frequency. Since sliding (kinetic) friction is usually nearly as strong as static (sticking) friction, it is also not necessary to apply precisely the value of torque which will result in the axle rolling without slipping along the side of the groove. These factors allow beginners to learn to speed up the rotation after only a few minutes of practice.

	By applying the proportionality of the force of friction to the normal force, <math>F_\mathrm{f} = \mu_\mathrm{k} F_\mathrm{n}</math>, where <math>\mu_\mathrm{k}</math> is the kinetic coefficient of friction, it can be shown that the torque spinning up the mass is a factor of <math>\mu_\mathrm{k} \left( r_{\mathrm{axle}} / R_{\mathrm{groove}} \right)</math> smaller than the torque applied to the shell. Since frictional force is essential for the device's operation, the groove must not be lubricated.<ref>Articles on ~~the physics of the device (in approximately increasing order of sophistication):~~
	* J.Higbie, ‘The physics of the “Dyna Bee”’, ''The Physics Teacher'', '''18''', 147–148 (1980).
	* P.G.Heyda, ‘Roller ball dynamics’, ''Mathematics Today'', '''36''', 9 (2000).
	* P.G.Heyda, [http://~~www~~.~~physics~~.~~princeton~~.~~edu~~/~~~mcdonald/examples/mechanics/heyda_ajp_70_1049_02.pdf ‘Roller ball dynamics revisited’~~]~~, ''American Journal~~ of ~~Physics'', '''70''', 1049–1051 (2002)~~.
	* D.W.Gulick & O.M.O’Reilly, [http:~~//www.hep.princeton.edu/~mcdonald/examples/mechanics/gulick_jam_62_321_00.pdf ‘On the Dynamics of the Dynabee’], ''ASME Journal of Applied Mechanics'', '''67''', 321–325 (2000).~~
	* T.Petrič, B.Curk, P.Cafuta, L.Žlajpah, [http://www.~~tandfonline~~.com/~~doi~~/~~abs~~/~~10.1080/13873954.2010.484237 ‘Modelling of the robotic Powerball : a nonholonomic, underactuated and variable structure~~-~~type system’], ''Mathematical and computer modelling of dynamical systems'', '''16''', 327–346 (2010)~~.
	<~~/ref~~>

	~~== References ==~~
	~~{{reflist}}~~

	~~==External links==~~
	~~{{Commons category\|Gyroscopic exercise tools}}~~
	*[http://straighttothebar.com/articles/2011/01/review_nsd_powerball/ NSD Powerball Gyroscope Review]
	*[http://www.~~nsd~~.~~com~~.~~tw/ Nanosecond website]~~
	*[http://www.~~nsdpowerus~~.com/ ~~NSD Spinner website]~~
	*[http://~~www.dansdata.com/gyrotwister~~.~~htm Review & Explanation of GyroTwister & Powerball]~~
	*[http://www.powerballeu.com/powerballdynabeeuitvinding.pdf Proof of patents and principle of working PDF in German]


	~~{{DEFAULTSORT:Gyroscopic Exercise Tool}}~~
	~~[[Category:Exercise equipment]]~~
	~~[[Category:Physical activity and dexterity toys]~~]

en>BG19bot: WP:CHECKWIKI error fix for #54. Do general fixes if a problem exists. - using AWB (9838)

2014-01-05T22:40:01Z

WP:CHECKWIKI error fix for #54. Do general fixes if a problem exists. - using AWB (9838)

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en>Ethilien: /* Basic op-amp diode circuit */ Correcting capitalization of variable names to match diagrams and the rest of the article

2012-05-31T23:58:39Z

Basic op-amp diode circuit: Correcting capitalization of variable names to match diagrams and the rest of the article

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