A unicyclist of total height h goes around a circular track of radius R while leaning inward at an angle \theta to the vertical. The acceleration due to gravity is g.
a. Suppose h \ll R. What angular velocity \omega must the unicyclist sustain?
b. Now model the unicyclist as a uniform rod of length h, where h is less than R but not negligible. This refined model introduces a correction to the previous result. What is the new expression for the angular velocity \omega ? 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 circle to the point of contact at the ground.