Meriam, Kraige & Bolton — Plane Kinematics of Rigid Bodies: Problem 5_41

5/41 Show that the expressions \( v = r\omega \) and \( a_t = r\alpha \) hold for the motion of the center \( O \) of the wheel which rolls on the concave or convex circular arc, where \( \omega \) and \( \alpha \) are the absolute angular velocity and acceleration, respectively, of the wheel. (Hint: Follow the example of Sample Problem 5/4 and allow the wheel to roll a small distance. Be very careful to identify the correct absolute angle through which the wheel turns in each case in determining its angular velocity and acceleration.)