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Let the lab frame be the frame where the dust is at rest. In an infinitesimal time interval

dT+dmΩ2r−GMPdmr2=0d cap T plus d m cap omega squared r minus the fraction with numerator cap G cap M sub cap P d m and denominator r squared end-fraction equals 0 Let the lab frame be the frame where the dust is at rest

Itotal=Irod+Iputty=748ML2+348ML2=1048ML2=524ML2cap I sub t o t a l end-sub equals cap I sub r o d end-sub plus cap I sub p u t t y end-sub equals 7 over 48 end-fraction cap M cap L squared plus 3 over 48 end-fraction cap M cap L squared equals 10 over 48 end-fraction cap M cap L squared equals 5 over 24 end-fraction cap M cap L squared Equating initial and final angular momentum: Let the lab frame be the frame where the dust is at rest

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