Chapter 16.1, Problem 16.47P

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

Fig. P16.47