Question
Derive the expression for moment of inertia of the thin rod about an axis through its center and perpendicular to its length.
Solution
Consider a rod of length 'L' and mass 'M'.
Let 'λ' be the linear mass density.
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Let a small line element dx be at a distance x from O.
Moment of inertia of this small line element of mass λdx about O is,
To find the total moment of inertia of rod, integrate from x = -L/2 to x = L/2.
I =
= 
Let 'λ' be the linear mass density.
Let a small line element dx be at a distance x from O.
Moment of inertia of this small line element of mass λdx about O is,
To find the total moment of inertia of rod, integrate from x = -L/2 to x = L/2.
I =
= 
