A unicyclist of total height h goes around a circular track of radius R while leaning inward at an angle θ to the vertical. The acceleration due to gravity is g.

A) Is h

Question

A unicyclist of total height h goes around a circular track of radius R while leaning inward at an angle θ to the vertical. The acceleration due to gravity is g.

A) Is h<<R, what angular velocity ω must the cyclist maintain?

B) Now, let the unicyclist be modeled as a uniform rod of length h, where h is less than R, but NOT negligible. What it the new result for the angular velocity ω? Assume that the rod remains in the plane formed by the vertical and radial directions, and that R is measured from the center of the center of the circle t

anonymous · Answer

(A) The normal force on the tract will have the components 
m r w^2 and m g and so tan@ = (r w^2 / g)  w = omega, angular velocity. The faster he goes, the greater @ is needed.