Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_59

7/59 The right-circular cone of height $h$ and base radius $r$ spins about its axis of symmetry with an angular rate $p$. Simultaneously, the entire cone revolves about the $x$-axis with angular rate $\Omega$. Determine the angular momentum $\mathbf{H}_O$ of the cone about the origin $O$ of the $x$-$y$-$z$ axes and the kinetic energy $T$ for the position shown. The mass of the cone is $m$.