A cicular disc of mass `m` and radius `R` is set into motion on a horizontal floor with a linear speed `v` in the forward direction and an angular speed `omega=(v)/(R)` in clockwise direction as shown in figure. Find the magnitude of the total angular momentum of the disc about bottom most point `O` of the disc.

Explanation

As we have discussed, angular momentum about `O` is the vector sum of two terms:
`Iomega` and `mvr_(bot)`
Here, `Iomega=I_(cm)omega=((1)/(2)mR^(2))((v)/(R))=(1)/(2)mvR` (perpendicular to paper inwards)
and `mvr_(bot)=mv_(c)r_(bot)=mRv` (perpendicular to paper inwards)
Since, both the terms are in the same direction
`L_("total")=(1)/(2)mvR+mvR`
or `L_("total")=(3)/(2)mvR` (perpendicular to paper inwards)