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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 the classical central-force problem of classical mechanics, some potential energy functions () produce motions or orbits that can be expressed in terms of well-known functions, such as the trigonometric functions and elliptic functions. This article describes these functions and the corresponding solutions for the orbits.
According to this equation, the second force F 2 (r) is obtained by scaling the first force and changing its argument, as well as by adding inverse-square and inverse-cube central forces. For comparison, Newton's theorem of revolving orbits corresponds to the case a = 1 and b = 0 , so that r 1 = r 2 .
Next Newton proves his "Theorema II" which shows that if Kepler's second law results, then the force involved must be along the line between the two bodies. In other words, Newton proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance.
The force exerted by the string can be resolved into a horizontal component, T sin(θ), toward the center of the circle, and a vertical component, T cos(θ), in the upward direction. From Newton's second law, the horizontal component of the tension in the string gives the bob a centripetal acceleration toward the center of the circle:
The force of tension applied to the spring, and the outward force applied to the drum by the spinning shoes are the corresponding reactive centrifugal forces. The mutual force between the drum and the shoes provides the friction needed to engage the output drive shaft that is connected to the drum. [ 7 ]
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.
All attractive central forces can produce circular orbits, which are naturally closed orbits. The only requirement is that the central force exactly equals the centripetal force, which determines the required angular velocity for a given circular radius. Non-central forces (i.e., those that depend on the angular variables as well as the radius ...