Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_84

6/84 In an investigation of whiplash resulting from rear-end collision, sudden rotation of the head is modeled by using a homogeneous solid sphere of mass \( m \) and radius \( r \) pivoted about a tangent axis (at the neck) to represent the head. If the axis at \( O \) is given a constant acceleration \( a \) with the head initially at rest, determine expressions for the initial angular acceleration \( \alpha \) of the head and its angular velocity \( \omega \) as a function of the angle \( \theta \) of rotation. Assume that the neck is relaxed so that no moment is applied to the head at \( O \).