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Question-116338




Question Number 116338 by Dwaipayan Shikari last updated on 03/Oct/20
Commented by Dwaipayan Shikari last updated on 03/Oct/20
Two thin circular discs of mass m and 4m ,having Radii a and 2a  respectively,are rigidly fixed by massless, rigid rod of length  l=(√(24))a,through their centres, tbis assembly is laid on a firm and flat  surface,and set rolling without slipping on the surface so that  the angular speed about of the rod is ′ω′. The angular momentum  of the entire assembly about the point ′O′ is ′L^→ ′  Find the Angular speed of the centre of mass of the assembly  rotates about z axis  And  Find the magnitude of angular momentum of the assembly  about its centre of mass
$$\mathrm{Two}\:\mathrm{thin}\:\mathrm{circular}\:\mathrm{discs}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{m}\:\mathrm{and}\:\mathrm{4m}\:,\mathrm{having}\:\mathrm{Radii}\:\mathrm{a}\:\mathrm{and}\:\mathrm{2a} \\ $$$$\mathrm{respectively},\mathrm{are}\:\mathrm{rigidly}\:\mathrm{fixed}\:\mathrm{by}\:\mathrm{massless},\:\mathrm{rigid}\:\mathrm{rod}\:\mathrm{of}\:\mathrm{length} \\ $$$$\mathrm{l}=\sqrt{\mathrm{24}}\mathrm{a},\mathrm{through}\:\mathrm{their}\:\mathrm{centres},\:\mathrm{tbis}\:\mathrm{assembly}\:\mathrm{is}\:\mathrm{laid}\:\mathrm{on}\:\mathrm{a}\:\mathrm{firm}\:\mathrm{and}\:\mathrm{flat} \\ $$$$\mathrm{surface},\mathrm{and}\:\mathrm{set}\:\mathrm{rolling}\:\mathrm{without}\:\mathrm{slipping}\:\mathrm{on}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{so}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{angular}\:\mathrm{speed}\:\mathrm{about}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rod}\:\mathrm{is}\:'\omega'.\:\mathrm{The}\:\mathrm{angular}\:\mathrm{momentum} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{entire}\:\mathrm{assembly}\:\mathrm{about}\:\mathrm{the}\:\mathrm{point}\:'\mathrm{O}'\:\mathrm{is}\:'\overset{\rightarrow} {\mathrm{L}}' \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{Angular}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{the}\:\mathrm{assembly} \\ $$$$\mathrm{rotates}\:\mathrm{about}\:\mathrm{z}\:\mathrm{axis} \\ $$$$\mathrm{And}\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{angular}\:\mathrm{momentum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{assembly} \\ $$$$\mathrm{about}\:\mathrm{its}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{mass}\: \\ $$

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