How Can I Calculate the Angular Speed of a Ring Rolling Without Slipping?

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To calculate the angular speed of a ring rolling without slipping, the center of mass moves in a circle of radius (R-r) around a point O. The angular speed of the ring's center is equal to the angular speed of the finger, denoted as ω0. The relationship between the angles of rotation of the finger (θ) and the ring (φ) is given by φ = θ(r/R). The angular speed of the ring about its center is determined by the difference in these angles, specifically ω = ω0(R-r)/R. Understanding the instantaneous axis of rotation (IAOR) is crucial, as the point of contact between the ring and the finger is momentarily at rest during rolling.
  • #31
zwierz said:
It seems that it is supposed that the ring remains in a horizontal plane. Strange
Yes, strange. I don't see how it could move in a truly horizontal plane.
 
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  • #32
it would be a good task to write honest equations of stationary motion that is when an angle of ring's incline is constant and the speed of ring's center is constant and ring's center moves along a horizontal cirle
 

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