This analysis combines forces and rotational mechanics to determine optimal pushing methods for a cylinder, highlighting applications in barrel races.
A circular cylinder is pushed by hand so that it rolls upward along an inclined plane. Newton’s second laws for translations and rotations are combined to find the required total pushing force as a function of both the point around the cross section of the cylinder at which that force is applied, and a coefficient of friction between one’s hands and the object. The optimum way to push the cylinder is subsequently deduced and compared to barrel races. A few special cases of the results are considered which are suitable for student exploration, such as in homework problems. The level of presentation is appropriate to an introductory calculus-based course in mechanics.
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Carl E. Mungan (2025) studied this question.
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