21–23 May 2018
Topland | Hotel & Convention Center Phitsanulok
Asia/Bangkok timezone

Shape sequence of rope coiling on a rotating plane

22 May 2018, 13:30
15m
Phichit Room

Phichit Room

Oral Statistical and Theoretical Physics A17: Statistical and Theoretical Physics

Speaker

Dr Sitichoke Amnuanpol (Physics department, Faculty of Science and Technology, Thammasat University)

Description

Rope fed uniformly from the height exhibits a perfectly circular coiling on a static plane. Introducing the rotation to the plane breaks the rotational symmetry of circle which gives rise to a variety of the more ordered patterns. For sufficiently fast feeding velocity v the coiling shape laying on a rotating plane is a hypotrochoid, namely a closed curve with exterior loops, when plane rotates slowly with low frequency f0. As f0 increases, the number of exterior loops decreases and the shape eventually turns to an epitrochoid, namely a closed curve with interior loops. The hypotrochoid-to-epitrochoid transition associates with a change in the sign of angular momentum. As f0 increases further, the number of interior loops gradually decreases to zero and the shape thus turns to a circle. Interestingly the circle which is the shape for static plane is restored at fast plane frequency f0, rather than at slow plane frequency f0 as our intuition would suggest. To elucidate the underlying principles, all the experimentally observed shapes, i.e. hypotrochoid, epitrochoid, and circle, are unified by a geometrical description. The key parameter which controls the shape is the ratio of the circumference velocity of plane relative to the feeding velocity, namely 2πf0R/v where R denotes the radius of the shape. The feeding velocity-plane frequency phase diagram is presented.

Author

Dr Sitichoke Amnuanpol (Physics department, Faculty of Science and Technology, Thammasat University)

Presentation materials

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