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When an automobile rounds a curve at high speed, the loading (weight distribution) on the wheels is markedly changed. For sufficiently high speeds the loading on the inside wheels goes to zero, at which point the car starts to roll over. This tendency can be avoided by mounting a large spinning flywheel on the car.
a. In what direction should the flywheel be mounted, and what should be the sense of rotation, to help equalize the loading? (Be sure that your method works for the car turning in either direction.)
b. Show that for a disk-shaped flywheel of mass m and radius R, the requirement for equal loading is that the angular velocity of the flywheel, ω_{0}, is related to the velocity of the car v by
where M is the total mass of the car and flywheel, and L is the height of the center of mass of the car (including the flywheel) above the. road. Assume that the road is unbanked.
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