00:01
So the total kinetic energy is the linear kinetic energy plus the rotational.
00:05
So half mv square plus half i omega square.
00:09
So we replace the v with v equals omega -r.
00:13
So replace the v with v square with omega -square with omega -square.
00:16
So that gives us this expression here.
00:18
And when you simplify this, we get this half omega -square multiplied by m -r -square plus i.
00:23
So this is the total kinetic energy.
00:25
And the fraction of rotational kinetic energy, we just divide the amount of amount rotational kinetic energy by the total energy here.
00:34
So if you do that we can see that the half and the omega square cancel out, we are left with a simpler expression, i over mr square plus i.
00:41
So let's look at the uniform cylinder.
00:44
So the moment of inertia i is half times mr square for uniform cylinder.
00:49
So you plug that in in place of i, then do the calculation that we had up here, i over mr square plus i.
00:55
So the mr squares cancel out, we're left with one -third.
00:58
So that's the fraction of kinetic energy for a solid cylinder.
01:01
Then for b, we do it for a sphere...