A rod has mass M and length L and a uniformdensity. Calculate the moment of inertia using theseequations:?

Question

A rod has mass M and length L and a uniformdensity. Calculate the moment of inertia using these equations:

1.) I= integral of (r ^2 dm)
2. the parallel axis theorem
I get different answers when I use both ofthose equations. I feel like I should get the sameanswer. Could someone explain how they used eachequation to obtain the answer? Thank yiu A rod has mass M and length L and a uniformdensity. Calculate the moment of inertia using these equations:

1.) I= integral of (r ^2 dm)
2. the parallel axis theorem
I get different answers when I use both ofthose equations. I feel like I should get the sameanswer. Could someone explain how they used eachequation to obtain the answer? Thank yiu

Explanation / Answer

If the rod is rotating lengthwise about its center of mass,the moment of inertia is I=(1/12)*M*L^2 If it rotates about an end, the moment of inertia isI=(1/3)*M*L^2 I'm not sure about the two methods that you're using, but theanswer should always be one of the above, regardless of your methodof obtaining it.

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