Example $7$:

An orthogonally bent slab without mass rotates at an angular velocity ${}_f,$ as depicted in the illustration. A wheel $($mass $m,$ radius $r,$ the spokes are without mass$)$ rotates at the end of the orthogonal slab in the $e_1^{**}-e_2^{**}-$plane at an angular velocity ${}_{\text{r}\text{e}\text{l}}.$

Complete both the components of the angular momentum vector with respect to the center of mass of the wheel, $L_S,$ and the components of the angular momentum vector to the center of mass of the wheel with respect to the point $P,L_{PR}.$

Given: $r=60cm,{}_{\text{r}\text{e}\text{l}}=\frac{201}{s},{}_f=\frac{91}{s},m=8kg,l=70cm$

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