Question

uniform disk turns at around a frictionless spindle. A nonrotating rod of three times of the disk mass and length equal to the disk’s diameter, is dropped onto the freely spinning disk, ( see Fig. ). They then turn together around the spindle with their centers superposed. What is the angular frequency in    of the combination?

Answer 1

so here angular momentum conservation

                       Li= Lf

                let disc of mass m and radius r and rotating around an axis perpendicular to plane of disc and passing through com with an angular velocity w

                 mr^2/2 w= ( MI OF ROD + MI OF DISC) W'

               mr^2/2 w = (3ml^2/12 + mr^2/2)W'

                    here l= 2r

              w'=w/3