Hello!

Non-scientist and Newbie to this forum, with what's probably an elementary engineering-type question, regarding torque. As a reference, I'm a life-long science buff, but I haven't had a course in physics since high school (I live in the USA)... more than fifty years ago.

As an example of the problem I'm attempting to resolve....

Assume a completely friction-free "see-saw" type of apparatus with the fulcrum fixed in position at the exact midpoint of a perfectly balanced rod. After placing a two-kilogram weight on each side of the rod, moderately close to but also equidistant from the fulcrum, the rod remains balanced.

The rod is then rotated about its fulcrum, and the amount of torque required to do so is calculated and measured.

One of the 2Kg weights is then removed, and a 1kg weight is added to that same side of the rod, at exactly twice the distance from the fulcrum point as was the original 2Kg weight... causing the system to once more be in balance.

The rod is again rotated about the fulcrum, and the amount of torque required to do so is again calculated and measured.

My contention -- based on my general and admittedly limited understanding of the the physics and math involved -- is that even though the weighted rod's actual center of gravity has been shifted... in both cases, the torque required to rotate the rod about its fixed fulcrum would be identical.

But I have been told that this is incorrect.

If so, could someone kindly explain -- in layman's terms, and/or using basic mathematics -- what it is that I'm misunderstanding?

I'm truly happy to have discovered this forum, by the way... and I thank you, in advance, for your kind indulgence!