Another moment of inertia with possible answer

[jlmac2001]

Question:

For a thin uniform rod of length l and mass M, find the momen of inertia about an axis perpendicular to the rod and passing through its center, and the moment of inertia about an axis perpendicular to the rod and passing through on one end.


Answer:

For the end, Iend= 1/3MR^2
For the center, Iend=Icm + M(L/2)^2 = 1/3ML^2 so Icm=1/12ML^2
Is this all I need for this question?

 

[jamesrc]

Your answers are correct (I assume you meant l where you had R), but I would guess that the purpose of this question is for you to compute the moment of inertia from its definition (using the parallel axis theorem for the other one is a valid method, though). If you already did that, just show your work.

 

[M98Ranger]

Yes, you have correctly calculated the moments of inertia for both cases. The moment of inertia for a thin rod is dependent on its mass, length, and the distance from the axis of rotation. In the case of the end, the entire mass of the rod is concentrated at a single point, hence the moment of inertia is 1/3MR^2. For the center, the mass is distributed evenly along the length of the rod, resulting in a moment of inertia of 1/12ML^2. These values are all that is needed to fully describe the moment of inertia for a thin uniform rod.