Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_156

6/156 The homogeneous sphere of Prob. 6/155 is placed on the incline with a clockwise angular velocity $\omega_0$ but no linear velocity of its center ($v_0 = 0$). Determine the time duration $t$ of the period of slipping. In addition, state the velocity $v$ of the mass center $G$ and angular velocity $\omega$ at the end of the period of slipping. (Reference to Prob. 6/155: The homogeneous sphere of mass $m$ and radius $r$ is projected along the incline of angle $\theta$ with an initial speed $v_0$ and no angular velocity ($\omega_0 = 0$). If the coefficient of kinetic friction is $\mu_k$, determine the time duration $t$ of the period of slipping. In addition, state the velocity $v$ of the mass center $G$ and the angular velocity $\omega$ at the end of the period of slipping.)