The force of gravity is not the same everywhere on Earth. It actually varies slightly from one location to another due to several factors, including the Earth's rotation and its shape. The phenomenon you mentioned about the difference in rotational speed between the equator and the North Pole does have an effect on gravity, but it is relatively small.
First, let's clarify that the force of gravity depends primarily on the mass of an object and the distance between that object and another mass. In the case of Earth, the force of gravity is caused by the Earth's mass and acts towards the center of the Earth.
Now, let's address the effect of Earth's rotation on gravity. As the Earth spins on its axis, there is a centrifugal force that opposes gravity. This centrifugal force is greater at the equator than at the poles because the speed of rotation is higher at the equator. However, it's important to note that the centrifugal force is not the same as gravity; it is a pseudo-force that arises due to the rotation of a non-inertial reference frame.
The effect of the centrifugal force on the overall gravity is relatively small. The difference in gravitational force between the equator and the poles due to the Earth's rotation is approximately 0.3%, which is a very small fraction. The primary reason for this small effect is that the gravitational force itself is much stronger than the centrifugal force.
Additionally, it's worth mentioning that gravity is not only determined by the Earth's rotation but also by the distribution of mass within the Earth. Variations in the density of Earth's materials, mountains, ocean currents, and other factors can cause slight variations in gravitational force from one location to another.
In summary, while the Earth's rotation does have an effect on gravity, the difference in gravitational force between the equator and the North Pole is relatively small compared to the overall force of gravity.