00:01
Hi, we have a uniform rod of mass m that is spinning around its center.
00:06
It has length l, so there are two other masses on the sides, m, m, and each of them are l half distance away from the center, and the total distance, total length of the rod itself is l.
00:19
Now we know that for the rod that is spinning around its center, the moment of inertia is m l square over 12.
00:27
We also know that for the compound system, the total moment of inertia must be equal to the inertia of the rod, which is m l square over 12, plus we have two masses, so two times m times the distance square, which is m of the masses times the distance for each of them is l half, and we need two squared.
00:47
So from here, we also know that this total moment of inertia must be equal to 0 .865.
00:54
So from here, we can already solve for l.
00:57
We can have here m l square over 12 plus m l square over 2 is equal to 0 .865.
01:07
And from here, here we have 12, so m l square plus 6 m l square is equal to 0 .865...