Problem $1.$ The upper $($hollow$!)$ semicircle has the radius $r$ and the mass $M.$ It rotates around its right edge point about the axis $($the red line, see Figure$)$ parallel to the axis $Y.$

a$)$ Found the moment of inertia $I_{CM}$ of the semicircle about the axis $Y,$ passing its center of mass.

b$)$ Found the moment of inertia I of the semicircle about the actual axis of its rotation $($the red line in Figure$).$

c$)$ Find the kinetic energy of the semicircle, if you know that one of its points $($which one?$)$ has the linear velocity $v,$ which is the maximal velocity among all other points. May you find the results in mathematical detail?