Parallel axis theorem is I = Io + Md^2
So say I have two spheres, equal weight and size, and I have a massless rod to hang them on. In one case I put the spheres on opposite ends and rotate about the middle of the rod -- it's really easy. In the second case I put both spheres on one end and try to rotate about the same point on the rod, it's much harder. This makes sense intuitively...
However, with a d-squared term, the moment of inertia shouldn't depend on where I put the spheres:
Case 1: I-total = Isphere + M(-D)^2 + Isphere + M(D)^2
Case 2: I-total = 2 * ( Isphere + M*(D)^2 ), which is the same.
But why, if the MOI is the same for both cases, is the balanced rod much easier to rotate?
It makes sense in my head, but not mathematically...
Thanks!
2007-10-18
07:25:59
·
1 answers
·
asked by
Michael
4