Chapter 16.1, Problem 16.24P

For a rigid body in centroidal rotation, show that the system of the inertial terms consists of vectors $-(\Delta m_i){\omega }^2{r^{\prime }}_i$ and $(\Delta m_i)(\alpha \times {r^{\prime }}_i)$ attached to the various particles P_i of the body, where ω and α are the angular velocity and angular acceleration of the body, and where ${r^{\prime }}_i$ denotes the position vector of the particle P_i relative to the mass center G of the body. Further show, by computing their sum and the sum of their moments about G, that the inertial terms reduce to a couple $\bar{I}\alpha$.

Fig. P16.24