Question

The moment of inertia of a uniform rod about an axis through its center is M L 2 / 12. The moment of inertia about an axis at one end is M L 2 / 3. Explain why the moment of inertia is larger about the end than about the center.

Answer 1

Answer:

the masses are far from the pivot point ,  its inertia to the movement is greater

Explanation:

The moment of inertia is defined by

               I = ∫ r² dm

For the rod it has different values ​​depending on where the axis is

End        I = 1/3 M L2

Center   I = 1/12 M L2

This difference is because the moment of inertia measures the resistance to rotation of a body to circular motion and is related to the distance of the masses to the point of rotation (axis).

In the case of the axis in the center that coincides by the center of mass the masses of one side and the other in equilibrium and a torque is needed to move each mass, so the torque is small to create the turning movement

But in the case of an external axle, all loads are on the same side and for the same, more torque is created to create the same turning movement

In general, the further the masses are from the pivot point, the more torque is needed to create a given movement (angular acceleration), so that its inertia to the movement is greater