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Related Concept Videos

Rolling Without Slipping01:09

Rolling Without Slipping

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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...
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Rolling With Slipping01:14

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Rolling with slipping is a physical phenomenon that occurs when a rolling object experiences both rotational and linear motion but also experiences frictional forces that cause slipping. This phenomenon can occur in various situations, such as when a tire rolls on a wet road or a ball rolls on a rough surface.
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Rolling Resistance01:21

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When a solid cylinder rolls steadily on a rigid surface, the normal force applied by the surface on the cylinder is perpendicular to the tangent at the contact point. However, since no materials are entirely rigid, the surface's reaction to the cylinder involves a range of normal pressures.
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Random Variables01:09

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A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
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The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
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Non-uniform Circular Motion01:22

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In uniform circular motion, the particle executing circular motion has a constant speed, and the circle is at a fixed radius. However, not all circular motion occurs at a constant speed. A particle can travel in a circle and speed up or slow down, showing an acceleration in the direction of motion. In that case, the motion is called non-uniform circular motion, and an additional acceleration is introduced, which is in the direction tangential to the circle. 
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Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
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Stochastic disks that roll.

Miranda Holmes-Cerfon1

  • 1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012, USA.

Physical Review. E
|December 15, 2016
PubMed
Summary
This summary is machine-generated.

Stochastic fluctuations alter particle rolling dynamics. Rolling constraints change equilibrium distributions, suggesting friction impacts thermodynamics or requires new modeling approaches for nanoscale systems.

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Area of Science:

  • Statistical mechanics
  • Soft matter physics
  • Nanotechnology

Background:

  • Stochastic fluctuations are crucial in nano/microscale systems.
  • Rolling motion can approximate strong static friction.

Purpose of the Study:

  • Investigate the impact of rolling constraints on particle dynamics under stochastic fluctuations.
  • Compare equilibrium distributions for sliding versus rolling particles.

Main Methods:

  • Developed a model of a three-disk polymer in a heat bath.
  • Used Langevin equations and homogenization theory.
  • Derived overdamped equations for configuration space dynamics.

Main Results:

  • Rolling constraints lead to different equilibrium distributions compared to sliding.
  • The dynamics resemble Brownian motion on manifolds.
  • Found a surprising difference in trimer equilibrium distributions.

Conclusions:

  • Rolling constraints significantly affect system thermodynamics.
  • Friction modeling with stochastic fluctuations requires careful consideration.
  • The term 'rolling' needs cautious use in stochastic systems.