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This reaction force is sometimes described as a centrifugal inertial reaction, [44] [45] that is, a force that is centrifugally directed, which is a reactive force equal and opposite to the centripetal force that is curving the path of the mass.
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
A centripetal force (from Latin centrum, "center" and petere, "to seek" [1]) is a force that makes a body follow a curved path.The direction of the centripetal force is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path.
The "reactive centrifugal force" discussed in this article is not the same thing as the centrifugal pseudoforce, which is usually what is meant by the term "centrifugal force". Reactive centrifugal force, being one-half of the reaction pair together with centripetal force, is a concept which applies in any reference frame.
The centrifugal force is given by the equation: = where m is the excess mass of the particle over and above the mass of an equivalent volume of the fluid in which the particle is situated (see Archimedes' principle) and r is the distance of the particle from the axis of rotation. When the two opposing forces, viscous and centrifugal, balance ...
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments) acting on the rigid body.
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 ...
In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian mechanics.