No, objects on the Earth's surface do not experience a downward centripetal force as a result of the Earth's rotation. While it is true that the Earth's rotation causes objects on its surface to move in a circular path, there is no additional centripetal force acting on those objects.
The force that objects experience due to Earth's rotation is called the "centrifugal force." However, it's important to note that the centrifugal force is not a real force in the sense of being an interaction between objects. Instead, it is a pseudo-force that arises from our observation in a rotating reference frame.
In reality, the only forces acting on objects on the Earth's surface are the gravitational force (weight) and the normal force exerted by the surface they are in contact with. The normal force, N, is equal in magnitude and opposite in direction to the weight (W) of the object. The normal force prevents the object from sinking into the surface and provides support against gravity.
So, the correct equation for the normal force is N = W, where N is the normal force and W is the weight of the object. The centripetal force does not need to be considered in this context, as it is not a relevant factor for objects on the Earth's surface.