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Rolling Without Slipping01:09

Rolling Without Slipping

People have observed the rolling motion without slipping ever since the invention of the wheel. For example, one can look at the interaction between a car's tires and the surface of the road. If the driver presses the accelerator to the floor so that the tires spin without the car moving forward, there must be kinetic friction between the wheels and the road's surface. If the driver slowly presses the accelerator, causing the car to move forward, the tires roll without slipping. It is essential...
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Rolling ribbons.

P S Raux1, P M Reis, J W M Bush

  • 1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Rolling elastic ribbons form a distinct peanut shape under critical forcing. This study combines experiments and theory to explain the ribbon

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Area of Science:

  • Physics
  • Materials Science
  • Fluid Dynamics

Background:

  • Elastic ribbons exhibit complex behaviors when subjected to external forces.
  • Understanding the morphodynamics of flexible materials is crucial in various scientific fields.

Purpose of the Study:

  • To investigate the steady shapes of rolling elastic ribbons under static and dynamic conditions.
  • To develop a theoretical model explaining the observed ribbon morphologies.

Main Methods:

  • Combined experimental and theoretical approaches were employed.
  • Analysis focused on characterizing steady shapes in rolling configurations.
  • A theoretical model was developed to rationalize observed shapes.

Main Results:

  • Above a critical forcing value (gravitational or centrifugal), ribbons adopt a stable two-lobed, peanut shape.
  • This shape is analogous to that observed in rolling droplets.
  • The model successfully rationalizes shapes based on bending and stretching dynamics.

Conclusions:

  • Elastic ribbon morphology is governed by bending and stretching under applied forces.
  • The study provides a framework for understanding the mechanics of rolling elastic structures.
  • The findings offer insights into shape transitions in deformable materials.