I'd never thought about this before, but once you calculate it, it is very small compared to g, the acceleration due to gravity:
The average circumference of the planet is about C = 40000 km.
Average speed of a point on the Equator due to this rotation V = 40000 / 24 km/h ~= 1700 km/h
Average radius of the Earth is approximately R = 6000 km, so the centripetal acceleration of the Equatorial point traveling at the tangential velocity of V is (V^2 / R) ~= 480 km/h/h ~= 0.04 m/s/s.
This acceleration is directed towards the center of the Earth, and is balanced by a fictitious force that goes in the opposite direction, making objects ever so slightly lighter.
However, this centripetal acceleration is very small compared to the acceleration due to gravity which is about g=9.8 m/s/s, which is why we don't "feel" it.
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