Question
Tue October 18, 2011 By:

can you please explain how the moment of inertia of a uniform rod is mr^2/12

Expert Reply
Wed October 19, 2011
) Moment of inertia of uniform rod about a perpendicular bisector
  • Consider a homogeneous and uniform rod of mass M and length L as shown below in the figure 

     

  • we have to calculate the moment of inertia of the rod about the bisector AB 
  • Consider middles point O to be the origin of the rod .Also consider an element of the rod between the distance x and x+dx from the origin. Since the rod is uniform so its density
    ?=M/L
    Hence mass of the element dm=(M/L)dx
  • Perpendicular distance of this element from line AB is x,so that moment of inertia of this element about AB is

     
  • For x=-L/2,the element is at the left end of the rod ,As x changes from -L/2 to +L/2 ,the element covers the whole rod
  • Thus the moment of inertia of the entire rod about AB is 
     
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