One evidence of the earth is rotating is the Coriolis Effect: 

"In physics, the Coriolis force is an inertial or fictitious force that acts on objects that are in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology."

"Italian scientist Giovanni Battista Riccioli and his assistant Francesco Maria Grimaldi described the effect in connection with artillery in the 1651 Almagestum Novum, writing that rotation of the Earth should cause a cannonball fired to the north to deflect to the east. In 1674, Claude François Milliet Dechales described in his Cursus seu Mundus Mathematicus how the rotation of the Earth should cause a deflection in the trajectories of both falling bodies and projectiles aimed toward one of the planet's poles. Riccioli, Grimaldi, and Dechales all described the effect as part of an argument against the heliocentric system of Copernicus. In other words, they argued that the Earth's rotation should create the effect, and so failure to detect the effect was evidence for an immobile Earth. The Coriolis acceleration equation was derived by Euler in 1749, and the effect was described in the tidal equations of Pierre-Simon Laplace in 1778.

Gaspard-Gustave Coriolis published a paper in 1835 on the energy yield of machines with rotating parts, such as waterwheels. That paper considered the supplementary forces that are detected in a rotating frame of reference. Coriolis divided these supplementary forces into two categories. The second category contained a force that arises from the cross product of the angular velocity of a coordinate system and the projection of a particle's velocity into a plane perpendicular to the system's axis of rotation. Coriolis referred to this force as the "compound centrifugal force" due to its analogies with the centrifugal force already considered in category one. The effect was known in the early 20th century as the "acceleration of Coriolis", and by 1920 as "Coriolis force".

In 1856, William Ferrel proposed the existence of a circulation cell in the mid-latitudes with air being deflected by the Coriolis force to create the prevailing westerly winds.

The understanding of the kinematics of how exactly the rotation of the Earth affects airflow was partial at first. Late in the 19th century, the full extent of the large scale interaction of pressure-gradient force and deflecting force that in the end causes air masses to move along isobars was understood."

             (from Wikipedia)

 Winds and the Coriolis Effect (LibreTexts)