A rod of mass `m` and length 2 R is fixed along te diameter of a ring of same mass `m` and radius R as shown in figure. The combined body is rolling without slipping along x-axis find the angular momentum about z-axis.

Explanation

Centre of mass of both lies at the centre of ring
`I_(C)=mR^(2)+(m(2R)^(2))/(12)`
`=(4)/(3)mR^(2)`
`L=(2mvr_(bot))+I_(C)omega`
`=(2mvR)+(4)/(3)mR^(2)((v)/(R))`
`=(10)/(3)mvR`
This is clockwise, or along negative z-axis.
`thereforeL=(-(10)/(3)mvR)hatk`