TY - JOUR
T1 - A jumping cylinder on an inclined plane
AU - Gómez, R. W.
AU - Hernández-Gómez, J. J.
AU - Marquina, V.
PY - 2012/9
Y1 - 2012/9
N2 - The problem of a cylinder of mass m and radius r, with its centre of mass out of the cylinders axis, rolling on an inclined plane that makes an angle α 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 < 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 < 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°, 30° and 45° 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.
AB - The problem of a cylinder of mass m and radius r, with its centre of mass out of the cylinders axis, rolling on an inclined plane that makes an angle α 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 < 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 < 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°, 30° and 45° 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.
UR - http://www.scopus.com/inward/record.url?scp=84864932490&partnerID=8YFLogxK
U2 - 10.1088/0143-0807/33/5/1359
DO - 10.1088/0143-0807/33/5/1359
M3 - Artículo
AN - SCOPUS:84864932490
SN - 0143-0807
VL - 33
SP - 1359
EP - 1365
JO - European Journal of Physics
JF - European Journal of Physics
IS - 5
ER -