关键词: 下滑时间, 阻力, 最速降线, 转动惯量

Abstract: We performe the dynamics analysis on sliding down time that affected by resistance. The famous branchistochrone is the fastest path which is obtained by ignoring resistance. Considering the sliding friction resistance and air resistance,we find that the sliding down time depends on the friction coefficient,amplitude of air restance, mass of object and slope of motion path. The sliding down time could be optimized by the radius of the circular orbital. On the other hand,  the scrolling down could also shorten the sliding down time, we also quantitatively investigate the scrolling time affects by the mass distribution of the disk and spherical shell, the mass distribution origins from the mass density and shape of the objects. The ratio of scrolling time to sliding time is decided by the function of mass density and the ratio of inside radii to outside radii.

Key words: sliding down time, frictional resistance, branchistochrone, rotational inertia