In the early days farmers used a “rolling mill” to ground grain. The grain was ground by a disk-shaped millstone that ro

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In the early days farmers used a “rolling mill” to ground grain.
The grain was ground by a disk-shaped millstone that rolled in a
circle on a flat surface, driven by a vertical shaft. Because of
the stone’s angular momentum, the contact force with the surface
(dashed line in the figure) was greater than the weight of the
wheel. Assume that the millstone rolls without slipping. Assume
that the millstone is a uniform disk of mass M, radius b, and width
w, and that it rolls without slipping in a circle of radius R with
angular velocity Ω. Find the ratio of the contact force with
respect to the surface to the weight of the stone.
(a) Draw a careful sketch of the free body diagram of both the
millstone and shaft system.
(b) Derive the expression for the angular momentum of the
millstone
(c) Derive the expression for the ratio of the contact force (N)
with respect to the surface to the weight of the millstone.