Angular and linear accelerations of a rolling cylinder acted by an external force

The dynamics of a cylinder rolling on a horizontal plane acted on by an external force applied at an arbitrary angle is studied with emphasis on the directions of the acceleration of the centre-of-mass and the angular acceleration of the body. If rolling occurs without slipping, there is a relationship between the directions of these accelerations. If the linear acceleration points to the right, then the angular acceleration is clockwise. On the other hand, if it points to the left, then the angular acceleration is counterclockwise. In contrast, if rolling and slipping occurs, the direction of the linear acceleration does not determine the direction of the angular acceleration. For example, the linear acceleration may point to the right and the angular acceleration clockwise or counterclockwise depending on the external force orientation and point of application.

Tilted boxes on inclined planes

We propose the study of a box placed on an inclined plane, with an initial tilt with respect to the plane. This is a paradigmatic example of the role played by friction as a link between translational and rotational motion. This example has two advantages over the usual example of a sphere (or cylinder) rolling down an inclined plane. First, it provides a good model for a much greater variety of "real-life" situations. Second, it exhibits a much richer structure in parameter space, even when the box starts from rest. (C) 2000 American Association of Physics Teachers.