# 114 X and O on Spinning Tube

For discussion’s sake, let’s say the tube was pressed on the X to set the tube rotating both about the Z and R axis, in the directions as depicted in the diagram below.

When the O is R-rotating on to the top, both its Z-rotation and R-rotation are causing it to move forward. The resultant velocity is thus increased. The O moves so fast it is blurred.

On the other hand, when the X is R-rotating on to the top, its Z-rotation is causing X to move forward, but the R-rotation is causing X to move backward. The resultant velocity is thus reduced. The X moves at a slow enough speed for our eyes to see it clearly.

From 0:44 onwards after O and X were written on transparency instead, both O and X are equally visible. Why? Well, the X is visible when it slows down as it R-rotates onto the top, whereas the O is visible when it slows down as R-rotates onto the bottom. So actually the O and X take turns to be visible, but persistence of vision means they both appear visible all the time.