Common Sense?

Say you support a uniform (negligible mass and thickness) rod at its center and hang an identical mass from each end. If you twist the rod by hand so it makes an angle, say 20 degrees, with the horizontal and then release it common sense tells us the rod will rotate to "find its balance" and after some up and down oscillation will end up horizontal. WHY? The gravity-produced torques on either end are always equal in magnitude and opposite in sense of rotation for any given angle. What else acts on the board to make it rotate at all? And it seems to be proportional to the angle because it is also common sense that at large angles the angular acceleration is greater than at small angles. What causes this acceleration?
- John Cheney
Fall River, MA USA

You have two lines of thought. One is common sense. The other is based on actual calculations of physical effects. I bet the calculations are right. The 'common sense' is probably left over from situations where the pivot was a little bit above the center of mass of a rigid object. Here it's at that center of mass. The rest of the mass, which is indeed lower than the pivot, doesn't make a rigid body here. The torques on the rod will be zero regardless of position.

Mike W,

(published on 02/28/2008)