자이로스코프 운동기구

자이로스코프 팔뚝 운동기구

자이로스코프 운동기구 (: Gyroscopic exercise tool) 는 손가락, 손바닥, 팔뚝의 힘을 기르기 위한 물리치료의 일환으로 손목을 단려하는 데 사용되는 도구이다. 이는 회전역학의 어떤 양상의 독특한 증명 수단으로도 사용될 수 있다. 테니스공 크기의 플라스틱이나 금속으로 된 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.

원리

이 장치는 구 모양의 껍데기와 그 안의 회전하는 질량으로 구성된다. 껍데기는 안의 질량체를 거의 완벽하게 덮어, 자이로스코프가 있도록 하는 작은 는다. 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.

회전하는 질량이 균형을 이루기 때문에, 회전 속도를 늘릴 수 있는 유일한 가능성은 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.게다가 수직항력, 축방향력은 어떠한 효과도 없으므로, 접선력은 마찰에 의해 제공되어야 한다. the normal and axial forces will have no effect, so tangential force must be provided by friction. 축이 안정적이라면 마찰은 회전을 감소시키는 방향으로만 작용하지만, 축이 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 in the plane of the groove or around an axis aligned with the axle, 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, ${\mathit {\Omega }}_{\mathrm {P} }R_{\mathrm {groove} }$, must exceed the relative speed due to the rotation of the spinning mass, $\omega r_{\mathrm {axle} }$. The minimum torque required to meet this condition is $I\omega ^{2}\left(r_{\mathrm {axle} }/R_{\mathrm {groove} }\right)$, where I is the moment of inertia of the spinning mass, and ω is its angular velocity.

회전의 가속이 적용된 토크의 방향에 관계 없이 발생하기 때문에, 장치는 토크의 크기가 충분하다면 어떠한 움직임의 미세조정 없이 기능할 것이다. 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.

수직항력과 마찰력의 비율을 적용하여, By applying the proportionality of the force of friction to the normal force, $F_{\mathrm {f} }=\mu _{\mathrm {k} }F_{\mathrm {n} }$, where $\mu _{\mathrm {k} }$ 은 is the kinetic coefficient of friction, it can be shown that the torque spinning up the mass is a factor of $\mu _{\mathrm {k} }\left(r_{\mathrm {axle} }/R_{\mathrm {groove} }\right)$ smaller than the torque applied to the shell. Since frictional force is essential for the device's operation, the groove must not be lubricated.

각주

This article "자이로스코프 운동기구" is from Wikipedia. The list of its authors can be seen in its historical and/or the page Edithistory:자이로스코프 운동기구. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.

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