A jumping cylinder on an inclined plane

作者：Gomez R W^*; Hernandez Gomez J J; Marquina V

来源：European Journal of Physics, 2012, 33(5): 1359-1365.

DOI：10.1088/0143-0807/33/5/1359

The problem of a cylinder of mass m and radius r, with its centre of mass out of the cylinder%26apos;s axis, rolling on an inclined plane that makes an angle a with respect to the horizontal, is analysed. The equation of motion is partially solved to obtain the site where the cylinder loses contact with the inclined plane ( jumps). Several simplifications are made: the analysed system consists of an homogeneous disc with a one-dimensional straight line mass parallel to the disc axis at a distance y %26lt; r of the centre of the cylinder. To compare our results with experimental data, we use a styrofoam cylinder to which a long brass rod is embedded parallel to the disc axis at a distance y %26lt; r from it, so the centre of mass lies at a distance d from the centre of the cylinder. Then the disc rolls without slipping on a long wooden ramp inclined at 15 degrees, 30 degrees and 45 degrees with respect to the horizontal. To determine the jumping site, the movements are recorded with a high-speed video camera (Casio EX ZR100) at 240 and 480 frames per second. The experimental results agree well with the theoretical predictions.

• 出版日期2012-9