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a rod of mass m and length l lies in the axis, with its centre at the origin. what is its moment of inertia about the line x=y?

a rod of mass m and length l lies in the  axis, with its centre at the origin. what is its moment of inertia about the line x=y?

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1 Answers

vikas askiitian expert
509 Points
11 years ago

dear reshab ,

 

first take elemental part dx anywhere on the rod & let the distance of this part from origin is x ..

 

angle bw rod & axis is @ = 45o (in this case)

 

perpendicular distance bw that part & axis is r = xsin@

 

mass of this element = m/l (dx)

 

dI (inertia of this small part) = (dm) r2

                                        = (m/l) (xsin@)2 dx

 

I = (msin2@/l) x2dx     lim from -l/2 to l/2

 

after integrating & putting limit we get

 

I = ml2 / 24

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