| Summary: | 碩士 === 國立臺中教育大學 === 科學教育與應用學系碩士在職專班 === 104 === This study focuses on the dynamics of the Gyro-Ring with the process divided into two stages including the theoretical derivation and experimental analysis. First, this study tried to develop the kinetic equation of Gyro-Ring , and then did the experimental research focused on the data related to the falling tracks of self-made ring and its precession rates both recorded with the image analysis software (Tracker Video) and high-speed camera. The result shows that the torque is equal to gravitational torque M gr_1 cosθ caused by friction delivers the rotational force of ring.The equations of motion of ring are:
I_1 (∅ ̈ sin〖θ+2〗 θ ̇∅ ̇ cos〖θ)〗=I_3 ω_3 θ ̇；〖(I〗_1+Mr_1^2)θ ̈+(I_3+Mr_1^2)ω_3 ∅ ̇ sinθ-〖 I〗_1 ∅ ̇^2 sinθ cosθ=-Mgr_1 cosθ；(I_3-Mr_1^2)ω ̇_3=-Mr_1^2 ∅ ̇θ ̇ sin〖θ.〗
Besides, this study also found that weight of ring has nothing to do with the precession rate, but is related to friction, inner radius, outer radius, height and tilt angle of ring, its speed can be expressed as ω_p=2√(((1-μ_p)gr_1)/([(〖r_1^2+r_2^2)+h^2/3]sin〗θ )) .In addition,precession rate of the ring must be fast enough to do the steady precession at the identical precession rate ∅ ̇,work as (I_3 ω_3 )^2≥4I_1 Mgr_1 cosθ ,under the condition of the fixed polar angle. Finally, this study found that the falling speed becomes faster as the weight of ring is heavier, the inner diameter larger, the outer diameter smaller and the fiction smaller.
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