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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 47586 (08)
- University: Sharif University of Technology
- Department: Mechanical Engineering
- Advisor(s): Jalali, Mir Abbas; Alam, Mohammad Reza
- Abstract:
- In this thesis we study an unexpected reverse spiral turn in the final stage of the motion of rolling rings. Equations of motion for rolling rings have been derived in the framework of Newtonian and Lagrangian mechanics, and solved in the presence of air drag forces and torques. The rolling motions of ellipsoids and disks have been used to validate the governing equations of motion. Based on experimental tests, we have found that the center of mass of rings moves in an S-shape trajectory. This is in contrast to spinning disks and coins that follow a spiral path before they stop. To explain this behavior, we included the effect of air drag in the equations of motions and found that the escape of the air through the ring’s central hole regulates the decay of angular momentum in the direction perpendicular to the disk’s plane. Consequently, the lateral component of the frictional force at the contact point gradually switches its direction and puts the ring around a new instantaneous center of rotation. This phenomenon is not observed for disks because they rapidly lose their angular momentum components along their diameters and maintain their initial spin direction. Our findings for rings are analogous to the flights of boomerangs, frisbees and soccer balls that move on curved trajectories. However, only boomerangs and rings experience a reverse turn. The results of this project can be used to design highly maneuverable speed boats and cars that experience both the air drag and the frictional forces of the sea surface or the ground
- Keywords:
- Rigid Body ; Pure Glide Motion ; Drag Coefficient ; S Shape Motion ; Retrograde Systems
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