Question

Moment of inertia of a rod about an axis passing through its one of end with their derivatation

Answer 1

Moment of Inertia (MI) of a rod about an axis passing its one end=1/3×ML^2 where M =mass of rod, L=length of the rod

• Derivation:

if mass of the rod = M

length=L

we know that MI of that rod about an axis through its middle point and perpendicular to the rod=1/12×ML^2

Now applying parallel axis theorem,

if the required MI of rod is= I

then according to the theorem,

I=1/12×ML^2+ M×(L/2)^2

or, I = 1/12×ML^2+ 1/4×ML^2

or, I= (1/12+1/4)ML^2

or, I= 1/3×ML^2

(Proved)