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A cicular disc of mass m and radius R is...


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.

Text Solution

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`vecL=vecL_(CM)+m(vecr_(0)xxvecv_(0))`……….i
here `vecL_(CM)=Iomega=(1/2mR^(2))(v/R)=1/2mvR` and `m(vecr_(0)xxvecv_(0))` (perpendicular to the paper inwards)
Since, both the terms of right and side of eq. i are in the same directon
`:. |vecL|=1/2mvR+mvR`
or `|vecL|=3/2mvR`
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