Moment of inertia, Physics

A non-uniform rod AB has a mass M and length 2l.The mass per unit lengthof the rod is mx at a point of the rod distant x from A. find the moment of inertia of this rod about an axis, a)through A,

b) through the mid point of AB.
 
Ans) let a element of length dx at adistance x from the point A of the rod.

mass of this element will be dm = mxdx

so moment of inertia of this element about point A is

  dI = dm * x2

for moment of inertia of whole rod perform intigration

I=  ∫dI = o2Ldm * x2

            =o2Lm * x3 dx

            =4mL4

and we know M =o2Ldm

                      = o2Lmxdx

                      =2mL2

so moment of inerta  I =2ML2

Posted Date: 3/8/2013 8:26:30 AM | Location : United States







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