Content deleted Content added
YesI'mOnFire (talk | contribs) Restored revision 1237875524 by Tito Omburo (talk): Rv to LGV |
|||
| (5 intermediate revisions by 4 users not shown) | |||
Line 1:
{{Short description|Device used in physical therapy}}
{{about|the gyroscopic exercise tool and toy|the US lottery|Powerball|other "powerballs"|Powerball (disambiguation)}}
[[Image:Gyrotwister.jpg|thumb|A gyroscopic wrist exerciser.]]
[[File:Video of a complete use session with a gyroscopic exercise tool.webm|thumb|Video showing the use - from starting the rotation with a 'shoestring' over various movements with the holding hand until stopping the rotor with the second hand. The demonstrated speeds are, in part, very high and not recommended for normal exercise due to the
A '''gyroscopic exercise tool''' is a specialized device used in [[physical therapy]] to improve wrist strength and promote the development of palm, wrist, forearm, and finger muscles. 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 surrounding a free-spinning mass, with an inner heavy core, which can be spun by a short rip string or using a self-start mechanism by means of rewinding it against a spring to give it [[potential energy]]. Once the [[gyroscope]] inside is going fast enough, the person holding the device can accelerate the spinning mass to high rotation rates by moving the wrist in a circular motion. The force enacted on the user increases as the speed of the inner gyroscope increases.
==Mechanics==
{{Disputed section|Friction based explanation is wrong|date = March 2025}}
{{Tone|date=March 2024}}
Inside the outer shell, the spinning mass is fixed to a thin metal [[axle]], each end trapped in a circular, equatorial groove in the outer shell. A lightweight ring with two notches for the axle ends rests in the groove. This ring can slip in the groove, allowing
To increase the [[angular velocity]] of the ball, the sides of the groove exert forces on the ends of the axle. The normal and axial forces will have no effect, so the tangential force must be provided by the [[friction]] of the ring acting on the axle. The user can apply a [[torque]] on the ball by tilting the shell in any direction except in the plane of the groove or around an axis aligned with the axle. The tilting 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 rate of rotation of the internal ball increases as the total amount of torque applied is increased. The direction of the torque does not matter, as long as it is perpendicular to the plane of rotation of the ball. The friction of the ring increases on
Since [[angular acceleration]] 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 rhythm with the precession or even have the same frequency. Since [[Friction|kinetic friction]] is usually almost as strong as [[Friction|static friction]] for the materials typically used, it is not necessary to apply exactly the amount of torque needed for the axle to roll 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 [[Friction|kinetic force of friction]] to the [[normal force]], <math>f_\mathrm{k} = \mu_\mathrm{k} F_\mathrm{n}</math>, where <math>\mu_\mathrm{k}</math> is the [[Friction#Coefficient_of_friction|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
==References==
{{reflist}}
| |||