Have you ever felt vertigo after a ride on a merry-go-round? Why can we feel this acceleration so intensively, while we do not notice at all that our very world does rotate around itself and rotate around the sun the entire time? This seems odd, considering that the Earth is travelling around the sun with a speed of approx. 30 km/s, while a merry-go-round is comparably slow with 8 m/s (see below).
First of all: What is “vertigo”? It is the perception of a (mock-)motion of oneself against the environment. Responsible for such cognition is the vestibular system which is able to recognise acceleration. In the labyrinth of this organ in the inner ear tiny hair is arranged in two planes: horizontal and vertical. It is embedded in a heavy matrix, which remains as it is in case of linear acceleration. Thus the hair experiences deflection and it comes to a sensory stimulus.
Rotatory acceleration is also recognized by sensory hair, which arranged in semi-circular canals which are filled with lymphatic fluid. If it comes to a rotation, this fluid remains (due to inertia) in contrast to the cranial bone. Thus the sensory hair is deflected and again we have a sensory stimulus.
So, now as we know about that, we need to clarify how the movement of the Earth is affecting us. The Earth carries out two kinds of movement: It rotates around the sun and around itself. If we assume a speed of 30 km/s (which is quite fast) and 365 days as a time period the Earth needs to travel around the sun, we can calculate an acceleration of approx. 1 mm/s2, which is very small, in deed. (For this calculation we neglect the fact that the speed is fluctuating.)
For the rotation of the Earth around itself we assume a perimeter of 40000 km. Since the rotation of the Earth around itself takes one entire day we have a speed of approx. 0.5 m/s and an acceleration of 5 μm/s2, respectively. This figure is even smaller than the one we calculated for the travel around the sun.
If we assume a merry-go-round with a diameter of 15 m and a velocity of 30 km/h the acceleration which the body experiences is 1.5 m/s2. This value is much higher than the acceleration of the Earth that is resulting from the travel around the sun and the rotation around itself.
I don’t know if I considered all effects that are somehow important to answer the question why we do not feel dizzy on our planet. But I think if one keeps in mind that it is not the speed but the acceleration that causes dizziness, the answer that I can give sounds reasonable.