Question
Derive the expression for moment of inertia of thin rod about an axis through its end and perpendicular to its length.
Solution
Consider a rod of length L and mass M.
Let λ be the linear mass density.
To find the total moment of inertia of rod, integrate from x = 0 to x = L
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 = 0 to x = L
