Rolling cylinder on a horizontal plane

Abstract

A cylinder on a horizontal plane, acted upon by a constant horizontal force, provides a variety of physical situations, which are helpful for understanding the behaviour and the role of friction in systems of particles. In our study, we consider rolling with and without slipping and establish the conditions for the frictional force to have the direction of the centre-of-mass velocity, contrary to the common idea that this force is always opposite to motion. In general, rolling without slipping requires static friction. However, under some conditions, rolling without slipping may take place even in the absence of a static frictional force. On the other hand, if the applied force and the kinetic frictional force fulfil certain relations, a pure translation of the cylinder may occur. The work done by friction is also discussed.

Rotation in secondary school: teaching the effects of frictional force

“…This problem has already been discussed by many authors (Shaw 1979, Caldas and Saltiel 1999a, Pinto and Fiolhais 2001, Mungan 2001, Hewitt 2002, Bartoš and Musilová 2004, although it has not been used as a teaching strategy for secondary school students. F has a non-zero component along the direction of motion (horizontal axis); its torque about the CM reinforces the translation motion.…”

Video-Based Analysis of the Transition from Slipping to Rolling

“…being the friction coefficient between the wheel and the ground. Combining equations (1), (2) and (3) gives μ the module of the frictional force and the linear acceleration of the centre of mass of the wheel on the x-axis, according to f = .m.g μ (4) a = .g μ (5)…”

Thermodynamics in rotating systems—analysis of selected examples

“…The forces are indicated in the figure -the two tensions are constant and equal in magnitude, T ′ = T , which establishes a connection between the two systems; the weight of each disc is G = M g and, since disc 1 has no translational motion, F = M g +T . For the rotation of disc 1, assuming that the discs are at rest for t = 0, equations (2) and (3) lead, after a trivial integration, to Indicated are the tension forces on the pulleys transmitted by the rope, T and T ′ , the weights, G, and the force, F , exerted by the support on the top pulley.…”

“…The mechanical system is the rotating wheel (including the cartridges and excluding the products of the gunpowder chemical reaction, which anyway are almost massless). For magnitude constant forces it is straightforward to apply equations (2) and (3) to the present example which, after integration, lead to…”