The Effect of Tangential Velocity on Ground-Contact Force: An Idealized Thought Experiment in Classical Mechanics

This paper presents an idealized thought experiment examining the relationship between tangential velocity and the force exerted between an object and a supporting surface. The analysis considers a small steel sphere near the surface of a perfectly spherical, non-rotating Earth, initially positioned one meter above the surface. The sphere is given progressively increasing tangential velocity while its mass and the gravitational field remain unchanged. For an object following a circular path of radius R, Newtonian mechanics gives the centripetal acceleration as a_c = v²/R. When the object is considered in contact with a spherical surface, the vertical force balance toward the center of the Earth can be expressed as N = mg − mv²/R, where N is the normal contact force. As the tangential velocity increases, the required centripetal acceleration increases. Consequently, gravity can provide an increasingly greater portion of the acceleration required for the object's curved trajectory, reducing the normal contact force. At the ideal circular-orbit condition, v²/R = g, and the normal force reaches zero. The analysis distinguishes gravitational force from contact force and examines why the familiar result N = mg for an object on a flat horizontal surface cannot be generalized to every possible geometry and state of motion. The paper does not propose a new fundamental law of physics. Rather, it uses an idealized thought experiment to demonstrate, using established Newtonian mechanics, that tangential velocity can affect the normal contact force under specific geometric and dynamical conditions. The discussion also examines the limitations of the idealized model, including Earth's curvature, atmospheric effects, Earth's rotation, the finite size of the object, and the physical impossibility of a finite-sized object literally orbiting while simultaneously occupying the Earth's solid surface.