So just a short video, a comment on the direction of the central fugal force. So let's go ahead and play with the math of it. So I've built another one of these little computer animations. So let's go ahead and do a cross-part. So let's go ahead and do a cross-part. So if I just move the vector so it's at the position of R, you see omega cross R. Look at this unsurprisingly. So let's move it back. So now what we want to do is omega cross R, cross omega. And then you rotate, bend your finger so it's a long omega. So there you go. Now as we watch it rotate around, notice omega cross R, cross omega, which multiply that by the mass of the particle and that is the centrifugal force on that particle. It is outward but it is not along the direction of R. It is away from the axis of rotation. And if you had thought about it, you would realize that's right. And in two dimensions, outward, and R, away from the axis of rotation, the same thing. But we have to be careful here because we're talking full three dimensions here. So the direction of the centrifugal force, just given the fact that you end with a cross-product with omega, it's got to be perpendicular to omega. So that's going to make it outwards away from the axis of rotation. So that's the direction of the centrifugal force. It's what you expected. By the way, if the centrifugal force were directly along R, then there wouldn't be any deflection from gravitational down to what you experience as down as a result of the centrifugal force on the Earth. But there is. And Taylor goes through all of that. Anyway, just a little quick thing to note the direction of the centrifugal force. And by popular request, water, see if you put water. Water is just a ticket. you