Finding Moment of Inertia of Rod

[Alem2000]

I had a problem with finding the moment of inertia. I have a rod and it has linear density$$\lambda=4.0kg$$ and the equation for its moment of inertia is $$I=\frac{1}{12} ML^2$$ now I have an axis at the center of mass of a rod the rod has a total length $$L=4m$$ so in my equation I would have to substute $$\lambda L=M$$ now the thing that I don't understand is if my center of mass horizontal cordinate is $$2m$$ the length I multipy by lambda should be 2m correct?

 

[Sirus]

Kg is not the unit for linear density. I'm assuming you meant $4.0\frac{kg}{m}$. If each meter of the rod has a mass of 4.0kg, why would you only multiply by half the length of the rod to get its mass? I think $M=(4.0\frac{kg}{m})(4.0m)$. Does that give you the right answer?

 

[GSXR750]

Yes, that is correct. The length that you use in the equation for moment of inertia should be measured from the axis of rotation to the outer edge of the object. In this case, since the axis is at the center of mass and the rod has a total length of 4m, the distance from the axis to one end of the rod would be 2m. Therefore, you would use 2m as the length in the equation. This is because the moment of inertia is a measure of an object's resistance to rotation, and the distance from the axis to the outer edge is what determines this resistance.