> We want to find the force at each tire. So by rearranging, we get F = PA. The pressure is gotten by a tire pressure gauge. Can someone explain why the air pressure inside the tire is the same as the pressure that the tire applies to the ground? Ignoring sidewall stiffness as pointed out to others, why must this be true?
It actually isn't true at all in practice. The inflation pressure and contact pressures vary dramatically even for a static tire due to curvature, tread depth, and many other factors. See e.g. https://www.sensorprod.com/news/white-papers/tcp/wp_tcp.pdf