The figure below shows four different cases involving a uniform rod of length L

Question

The figure below shows four different cases involving a uniform rod of length L and mass M is subjected to two forces of equal magnitude. The rod is free to rotate about an axis that either passes through one end of the rod, as in (a) and (b), or passes through the middle of the rod, as in (c) and (d). The axis is marked by the red and black circle, and is perpendicular to the page in each case. This is an overhead view, and we can neglect any effect of the force of gravity acting on the rod. Rank these four situations based on the magnitude of the rod's angular acceleration, from largest to smallest. Use only > and/or = signs in your rankings, such as c>b=d>a.

I keep getting the answer incorrect. Isn't it a>d>b=c?

Explanation / Answer

In my last answer, I neglected the effect of the moment of inertia. Again, the torques for each cases are (a) 2Fr (b) Fr (c) 2Fr (d) Fr Moment of inertia for each cases are (a) 1/3M(2r)^2 (b) 1/3M (2r)^2 (c) 1/12M(2r)^2 (d) 1/12M (2r)^2 Angular acceleration is torque divided by moment of inertia. The ratio between these guys become (a)6 (b)3 (c) 24 (d)12 Therefore the answer is c>d>a>b

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