Suppose a uniform slender rod has length L and mass m. The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by Icm= 1/2mL^2. Required:
Find Icmd the moment of inertia of the rod with respect to a parallel axis through one end of the rod.

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(mI^2)/3

Explanation:

The parallel axis theorem for the calculation of inertia is: I = I CM + Md^2

So, I is the apathy from an axis that is at distance d from the center of mass and LCM the apathy when the axis passes through the center of mass. Do to this, the axis passes through the end of the rod. In analysis, d=l/2

So, we have the equation:

I = mI^2/12 + m (1/2)^2 = mI^2/12 + mI^2/4 = mI^2/12 + 3mI^2/12 = mI^2/3

This relents us the terminal result: (ml^2)/3.

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