The expression 'centrifugal force' can in most circumstances be understood as: 'a centripetal force is required'.
In the case of the spinning Earth:
At the equator the measured gravitational acceleration is a slightly lower value than the measured gravitational acceleration at the poles.
At the Equator: 9.7805 $m/s^2$
At the poles: 9.8322 $m/s^2$
About one third of the difference is due to the fact that an object located on the Equator is about 21 kilometers further away from the Earth's geometric center than an object at (either one of) the poles. (Due to its rotation the Earth has an equatorial bulge.)
But the main part of the difference is as follows: to be co-rotating with the Earth at the Equator requires a centripetal acceleration. Providing that centripetal acceleration goes at the expense of the gravitational acceleration.
The acceleration that is required to circumnavigate the Earth's axis along the equator, at one revolution per sidereal day, is 0.0339 $m/s^2$.
From that we can infer that the newtonian gravitational acceleration at the Equator must be 9.8144 $m/s^2$
We can only infer that value, due to the equivalence of inertial and gravitational mass. Because of that equivalence some things are not accessible to measurement. A single measurement cannot inform you whether some of the gravitational acceleration is expended in providing required centripetal acceleration.
Throughout the history of mechanics the equivalence of inertial mass and gravitaional mass has been among the most important factors.
Historically:
Newton had formed the hypothesis of an inverse square law of gravity. In terms of Newton's law of Universal Gravity: the gravitational acceleration experienced by a planet is proportional to the gravitational mass of that planet. So: does that mean that Newton had to know the mass of each planet? Newton had the following insight: if inertial mass and gravitational mass are equivalent then in order to verify the concept of a universal inverse square law of gravity it is not necessary to know the mass of each planet.
The amount of required centripetal force for a planet to remain in orbit is proportional to the inertial mass. If gravitational mass and inertial mass are equivalent then the mass drops out of the calculation.
Returning to measurement:
A very interesting physical effect that arises from the Earth's rotation is called the Eötvös effect, after the Hungarian scientist Loránd Eötvös.
Eötvös developed instruments for gravimetry, his instrument were very sensitive.
Quoting from the wikipedia article:
In the early 1900s, a German team from the Geodetic Institute of Potsdam carried out gravity measurements on moving ships in the Atlantic, Indian, and Pacific oceans. While studying their results, the Hungarian nobleman and physicist Baron Roland von Eötvös (Loránd Eötvös) noticed that the readings were lower when the boat moved eastwards, higher when it moved westward.
When you have a velocity with respect to the Earth (such as the velocity of a ship), in eastward direction, you are circumnavigating the Earth at an angular velocity slightly larger than the angular velocity of the Earth itself.
That slightly larger angular velocity has a correspondingly larger requirement for centripetal acceleration. That is what Eötvös recognized in the measurement data.
The required centripetal acceleration goes at the expense of gravitational effect.
I noticed that in another answer the theory of General Relativity was mentioned in a byline.
Obviously General Relativity is outside the scope of this question, but let me make a few remarks.
General Relativity frames the equivalence of inertial mass and gravitational mass at a whole different level.
Still: some things from the newtonian theory carry over to GR.
There is the notion of a gravitationally bound system. There is a hierarchy of nested levels.
The Earth-Moon system is a gravitationally bound system
Next level up: the Solar system
Next level up: our Galaxy; the stars of our Galaxy are all orbiting the center of mass of the Galaxy.
For the planets of the solar system: Retrograde motion is apparent motion.
Incidentally: when the circumference of the Earth is known the angular velocity of the Earth can be inferred by capitalizing on the earlier mentioned Eötvös effect.
On a non-rotating planet there is no Eötvös effect: two ships, moving in opposite direction (with equal velocity wrt the surface), will measure the same gravitational acceleration.
On a rotating planet: the difference in measured value between moving in eastward direction and moving in westward direction is proportional to the angular velocity of the planet. Obtain a measurement of that difference, combining with known circumference allows you to infer the rotation rate of the planet.