How would a motorcycle ride in a horizontal circle?
There are circus acts in which the motorcycle is being ridden around a horizontal ring. You might think that that's the equivalent of your diagram with a theta of 90 degrees. But what actually happens is that the motorcycle is not pointing at the center of the ring, but at a point slightly above the center of the ring. That has to be done to provide the upward force required to counteract the weight of the motorcycle and rider. The faster the motorcycle goes, the smaller this above the center angle needs to be. In your diagram, you're actually ignoring the weight of the motorcycle and rider. If that was being taken into account, that line from the point of contact through the rider would not be pointing at the center of the sphere, it would be pointing just above the center of the sphere.
