We show that rapidly rotating cylinders sliding on smooth surfaces can exhibit novel trajectories. The lateral deflection can be as large as the net displacement in the initial direction of motion. With a large enough initial angular speed, the cylinder can trace out a spiral trajectory having a large number of loops. An exact analytical result for large lateral deflection is also derived. PACS No.: 4600

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We compare the exact tunneling time with the quasi-classical tunneling time for idealized potentials. We examine three one-dimensional cases where the potential is chosen to have a simple form. In each case, the exact tunneling time and the quasi-classical time differ significantly. In one case, the two differ in magnitude by a factor of about ten. In another case, the two differ not only quantitatively, but qualitatively as well. A discussion is given as to why the two times are significantly different, and suggestions for further inquiries are made. PACS Nos.: 03.65Xp, 03.65-w

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