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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.
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 .
The central-force problem concerns an ideal situation (a "one-body problem") in which a single particle is attracted or repelled from an immovable point O, the center of force. [4] However, physical forces are generally between two bodies; and by Newton's third law, if the first body applies a force on the second, the second body applies an ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun.
A central-force problem is said to be "integrable" if this integration can be solved in terms of known functions. If the force is a power law, i.e., if F ( r ) = a r n {\displaystyle F(r)=ar^{n}} , then u {\displaystyle u} can be expressed in terms of circular functions and/or elliptic functions if n {\displaystyle n} equals 1, -2, -3 (circular ...
Unlike the inertial force known as centrifugal force, which exists only in the rotating frame of reference, the reactive force is a real Newtonian force that is observed in any reference frame. The two forces will only have the same magnitude in the special cases where circular motion arises and where the axis of rotation is the origin of the ...
Eliminating the angular velocity dθ/dt from this radial equation, [47] ¨ = +. which is the equation of motion for a one-dimensional problem in which a particle of mass μ is subjected to the inward central force −dV/dr and a second outward force, called in this context the (Lagrangian) centrifugal force (see centrifugal force#Other uses of ...