00:01
Okay, so we want to figure out the centre of mass of this shape.
00:04
Now, i'm going to call, because the picture that you've uploaded is very blurry, i can't see how the various different parts of the drawing are labelled.
00:16
So what i'm going to do is i'm going to give my own labels, and then hopefully they equate to the ones on your diagram, or if not, you can just replace them with the letters that you've been given there.
00:26
So i'm going to call the full length l.
00:28
I'm going to call the radius of this top circle r1, the radius of the bottom circle r2, and the width here, x.
00:41
So if i call the origin, the point here, so this i'll call the point zero zero, then the x center of mass is clearly just going to be r2, because the center of mass for each of the three components, so i'm going to be splitting this shape up into three components, the bottom, the bottom, one, which i'll call shape 1, the middle one which i'll call shape 2, and the top one which i'll call shape 3.
01:17
And all of them have the centre of mass along this line here, which is at r2 0.
01:28
So the x centre of mass is going to be r2.
01:31
For the y centre of mass, it's a little bit trickier.
01:35
What we do is we do the centre of mass for shape 1 times the mass of shape 1 plus the centre of mass for shape 2 times the mass of shape 2 plus the same for shape 3, and then divide it by the total mass.
01:54
And the centre of mass for the first shape, the y center of mass for the first shape, is just r2, clearly, because the centre of mass is the centre of the circle, which is r2 off the floor.
02:04
And the mass of that shape is just pi r2 squared...