$11\mathrm{.}17$ Optional: Angular momentum and kinetic energy of a rigid body with a simple vec$().$

The following figure shows right$-$handed orthogonal unit vectors widehat$(b{)}_x,$widehat$(b{)}_y,$widehat$(b{)}_z$ fixed in a rigid body $B$ which rotates in a reference frame $N$ with a simple angular velocity ${?}^N$vec$({)}^B={}_z$widehat$(b{)}_z.$ Point $B_p($not shown$)$ is a generic point of $B$ that is either $B_{cm}(B\text{'}$s center of mass$)$ or fixed $($not moving$)$ in $N.B\text{'}$s inertia dyadic and inertia matrix about $B_p$ can be expressed in terms of $B\text{'}$s moments and products of inertia