Centripetal Force

$$\text{Carousel Day}$$

Today (July 25) is National Carousel Day!

You approach the average looking carousel with trepidation. Its radius is 4.8768 meters. Your mass is 70 kilograms. You step up to a plain looking horse and mount it. The carousel begins to spin. And spin. And spin. Suddenly, it's breaking the sound barrier and going supersonic. The velocity is clearly 343 meters per second.