“Why are we not feeling Earth’s rotation while it is actually happening”
It is just like we don’t feel like moving when we are inside a train moving with constant velocity and especially when we are not looking out of the window.
When we look out from earth, we see stars and other heavenly bodies which are very much far away and the relative change in position is very much less to be noticeable.
The most celebrated test of Earth’s rotation is the Foucault pendulum first built by physicist Léon Foucault in 1851, which consisted of an iron sphere suspended 67 m from the top of the Panthéon in Paris. Because of the Earth’s rotation under the swinging pendulum the pendulum’s plane of oscillation appears to rotate at a rate depending on latitude. At the latitude of Paris the predicted and observed shift was about 11 degrees clockwise per hour. Foucault pendulums now swing in museums around the world.