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Kanchana Atapattu Grade: Upto college level
        

Find the moment of  inertia of a lamina bounded by concentric circles of radii a and b about a diameter.

8 years ago

Answers : (1)

ashish kumar
13 Points
										

Let the mass of the lamina be m.


Therefore the density of the lamina § = m/¶(b2-a2).





Consider an element of thickness dr at adistance r from the centre.


                                                                             dm = §(2¶rdr)


Therefore moment of inertia about the centre O


                             I = dmr2


                              = §(2¶rdr)r2


                            = 2§¶r3dr


                                   = 2§¶(b4-a4)/4


                                   = 2m¶(b4-a4)/(4¶(b2-a2))


                            = m(a2+b2)/2


 Applying the perpendicular axis theoram




                                                                                     Iz = Ix + Iy


Io = Iab + Icd


  By symmetry Iab = Icd


Iab = Icd = Io/2


= m(a2+b2)/4


8 years ago
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