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The rope example is an example involving a 'pull' force. The centripetal force can also be supplied as a 'push' force, such as in the case where the normal reaction of a wall supplies the centripetal force for a wall of death or a Rotor rider. Newton's idea of a centripetal force corresponds to what is nowadays referred to as a central force.
In classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field.A central force is a force (possibly negative) that points from the particle directly towards a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center.
The component of weight force is responsible for the tangential force (when we neglect friction). The centripetal force is due to the change in the direction of velocity. The normal force and weight may also point in the same direction. Both forces can point downwards, yet the object will remain in a circular path without falling down.
In a two-body rotation, such as a planet and moon rotating about their common center of mass or barycentre, the forces on both bodies are centripetal. In that case, the reaction to the centripetal force of the planet on the moon is the centripetal force of the moon on the planet. [6]
The Kepler problem and the simple harmonic oscillator problem are the two most fundamental problems in classical mechanics. They are the only two problems that have closed orbits for every possible set of initial conditions, i.e., return to their starting point with the same velocity (Bertrand's theorem). [1]: 92
The second section establishes relationships between centripetal forces and the law of areas now known as Kepler's second law (Propositions 1–3), [21] and relates circular velocity and radius of path-curvature to radial force [22] (Proposition 4), and relationships between centripetal forces varying as the inverse-square of the distance to ...
When calculating a maximum velocity for our automobile, friction will point down the incline and towards the center of the circle. Therefore, we must add the horizontal component of friction to that of the normal force. The sum of these two forces is our new net force in the direction of the center of the turn (the centripetal force):
It is only in very special circumstances that the vector of the centripetal force and the centrifugal term drop away against each other at every distance from the center of rotation. This is the case if and only if the centripetal force is a harmonic force. In this case, only the Coriolis term remains in the equation of motion.