A water wheel with radius Rw $=1\mathrm{.}1$ m and mass Mw $=1\mathrm{.}25$ x $103$ kg is used to power a grain mill next to a river. Treat the water wheel as a hollow cylinder. The rushing water of the river rotates the wheel with a constant frequency fr $=2\mathrm{.}2$ Hz$.$

Part $($a$)$

Calculate the angular velocity $\backslash$omega w of the water wheel in radian$($s$)/($sec$.)$

$$ Part $($b$)$

Calculate the kinetic energy Kw$,$ in J$,$ of the water wheel as it rotates.

$$ Part $($c$)$

Assume that every second, $20\%$ of the kinetic energy of the water wheel is transmitted to the grain mill. Calculate the power Pw in W of the grain mill based on the energy it receives from the water wheel.