For a rigid slab in centroidal rotation, show that the system of the effective forces consists of vectors -\left( \Delta { m }_{ i } \right) { \omega }^{ 2 }{ r }_{ i }^{ \prime } and \left( \Delta { m }_{ i } \right) (\alpha \times { r }_{ i }^{ \prime }) attached to the various particles { P }_{ i } of the slab, where \omega and α are the angular velocity and angular acceleration of the slab, and where { r }_{ i }^{ \prime } denotes the position vector of the particle { P }_{ i } relative to the mass center G of the slab. Further show, by computing their sum and the sum of their moments about G, that the effective forces reduce to a couple \overline { I } \alpha.