Halliday, Resnick & Walker — Vectors: Problem 69

A wheel with a radius of $45.0\text{ cm}$ rolls without slipping along a horizontal floor (Fig. 3.17). At time $t_1$, the dot $P$ painted on the rim of the wheel is at the point of contact between the wheel and the floor. At a later time $t_2$, the wheel has rolled through one-half of a revolution. What are (a) the magnitude and (b) the angle (relative to the floor) of the displacement of $P$?