Related papers: Slipping and Rolling on an Inclined Plane
The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…
We show that two basic mechanical processes, the collision of particles and rolling motion of a sphere on a plane, are intimately related. According to our recent findings, the restitution coefficient for colliding spherical particles…
A first-principle continuum-mechanics expression for the rolling friction coefficient is obtained for the rolling motion of a viscoelastic sphere on a hard plane. It relates the friction coefficient to the viscous and elastic constants of…
We study the motion of a two-dimensional droplet on an inclined surface, under the action of gravity, using a diffuse interface model which allows for arbitrary equilibrium contact angles. The kinematics of motion is analysed by decomposing…
We present a model for the motion of hard spherical particles on a two dimensional surface. The model includes both the interaction between the particles via collisions, as well as the interaction of the particles with the substrate. We…
This article illustrates the role of friction on the motion of a rolling sphere on pedagogical example. We use a parabolic support rotating around it axis to study the static equilibrium positions of a single sphere. Due to the particular…
We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…
Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than…
A small sphere placed on the top of a big static frictionless sphere, slips until it leaves the surface at an angle $\theta_{l}=\cos^{-1}{2/3}$. On the other extreme, if the surface of the big sphere has coefficient of static friction,…
By means of Molecular Dynamics simulations, we investigate the elementary process of avalanches and size segregation by surface flow in 2 dimensions: a single ball confined to moving along an inclined line consisting of balls. The global…
Motion of a point particle sliding on a turntable is studied. The equations of motion are derived assuming that the table exerts frictional force on the particle, which is of constant magnitude and directed opposite to the direction of…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
The motion of a block slipping on a surface is a well studied problem for flat and circular surfaces, but the necessary conditions for the block to leave (or not) the surface deserve a detailed treatment. In this article, using basic…
We experimentally investigate the dynamics of a sphere rolling down a granular slope by varying the initial velocity, slope angle, and sphere density. The results show that the sphere rolls down with constant deceleration while sinking into…
The idea of contact angle was generalized by using the principle of minimum total energy. The problems of the shape of the two-dimensional sessile drop and the drop on an inclined surface are considered. The differential equations…
We calculate the friction force acting on a hard cylinder or spherical ball rolling on a flat surface of a viscoelastic solid. The rolling friction coefficient depends non-linearly on the normal load and the rolling velocity. For a cylinder…
We experimentally investigate the dynamics of a sphere rolling up a granular slope. During the rolling-up motion, the sphere experiences slipping and penetration (groove formation) on the surface of the granular layer. The former relates to…
We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both…
A particle is thrown tangentially on a surface. It is shown that for some surfaces and for special initial velocities the thrown particle leaves immediately the surface, and for special conditions it never leaves the surface. The conditions…
A computational study of sliding blocks on inclined surfaces is presented. Assuming that the friction coefficient $\mu$ is a function of position, the probability $P(\lambda)$ for the block to slide down over a length $\lambda$ is…