The equations describe the motion, velocity and acceleration of a point on a rotating body with an additional linear motion of speed vl in the x-direction. R is the distance of point P from the center of rotation, ω is the rotation angular speed.
As we can see, the linear motion does not contribute to the acceleration. Therefore we can not feel or measure the linear motion with an accelerometer, neither in the nonrotating nor in the rotating frame of reference of the moving body.
If P is an observer on the surface of the rotating earth, in his rotating frame of reference he feels the sum of 2 accelerations: the gravitational acceleration towards the center of the earth and the much smaller constant centrifugal acceleration in the direction away from the axis of rotation and the same magnitude as the centripetal acceleration. The result is a slightly smaller effective gravitational acceleration which points not exactly to the center of the earth, except on the equator and the poles. This effective gravitational acceleration is the only thing we can feel on a rotating earth orbiting the sun in free fall (or a constant linear speed).