(Solved): A child with mass m=35kg is playing on a rotating merry-go-round with mass M=270kg and radius R ...

A child with mass $m=35\mathrm{kg}$ is playing on a rotating merry-go-round with mass $M=270\mathrm{kg}$ and radius $R=3\mathrm{m}$. The pivot is frictionless and the merry-go-round and child are rotating together with angular speed $\omega =2.2\mathrm{rad}/\mathrm{s}$. The child is standing at $r_{\text{child }}=\frac{3}{4}R$, as shown in the figure. If we model the child as a point mass $\left(I=M{R}^2\right)$ and the merry-go-round as a disk $\left(I=\frac{1}{2}M{R}^2\right)$, what is the magnitude of the total angular momentum of the child + merry go round system? (a) $L=2673\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}\times$ (b) $L=3192.75\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}\times$ (c) $L=2283.19\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}$ (d) $L=3062.81\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}$ (e) $L=857.59\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}$ Select all possible options that apply. There is exactly 1 correct option in the list above. This question is complete and cannot be answered again. Correct answer (d) $L=3062.81\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}$