Question

Find moment of inertia of thin uniform rod of mass m and length I rotating about perpendicular axis passing through centre of mass.
Please help me mates ​

Answer 1

We know, a thin uniform rod lying on the axis that is passing through its center have a moment of inertia,

I(XY) = mL2/12

Where, m is the mass per unit length of the rod and L is the length of the rod.

Let us assume that the endpoint of the rod lies on the point (P, Q) and the moment of inertia at that point is I′.

I = mL2/12

m is the total mass.

By applying the parallel axis theorem, we have-

I′ = I + m(L/2)2

Since the distance from the center to the endpoint is 2L.

I′ = (mL2)/12 + (mL2)/4

= mL2(1/12 + 1/4)

= 4(mL2/12)

= 4I

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