00:01
All right, in this problem, they want us to find the axis of gyration for all the different shapes.
00:07
So let's start with something simple, like the thin hoop.
00:18
Okay.
00:19
And for all of these, we'll say it has a radius of r not.
00:24
Okay? so we're going to have mk squared equal to m r not squared.
00:36
For our rotational inertia.
00:38
So in this case, what we'll do is we'll solve this for k, and so we'll get k equals r not.
00:48
Because you'll notice that the m's will cancel, like such, and then you can take the score where you each side.
00:53
And so there is your answer for a thin hoop.
00:58
With the solid cylinder, like that, all right, we're going to start up with m, k, squared again, and that should be equal to one -half m r squared.
01:29
Okay, m's cancel, square root each side, and so we'll get k equal to the square root of one -half r -not.
01:40
So there we go.
01:43
That's it for that one.
01:44
All right.
01:45
Now let's do a howl sphere, or excuse me, a howl cylinder, my fault.
01:55
Howl cylinder.
02:00
Okay.
02:01
That's the case.
02:02
For the hollow cylinder, we're going to start with m k squared is equal to one -half m, and we have the inner radius squared plus the outer radius.
02:22
It's squared.
02:23
Okay, so m still cancel, like such, square each side.
02:28
So you'll have k equal to square root of one -half, and i can't even touch these.
02:36
It's going to stay the same.
02:37
Just like that.
02:42
Just like that.
02:43
All right...