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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.
Vectors are defined in cylindrical coordinates by (ρ, φ, z), where . ρ is the length of the vector projected onto the xy-plane,; φ is the angle between the projection of the vector onto the xy-plane (i.e. ρ) and the positive x-axis (0 ≤ φ < 2π),
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler. Their general vector form is
The resultant force provides required centripetal force. Without this centripetal force frictionless objects would slide towards the equator. In calculations, when a coordinate system is used that is co-rotating with the Earth, the vector of the notional centrifugal force points outward, and is just as large as the vector representing the ...
Newton's vectorial approach to mechanics describes motion with the help of vector quantities such as force, velocity, acceleration. These quantities characterise the motion of a body idealised as a "mass point" or a " particle " understood as a single point to which a mass is attached.
Centripetal force causes the acceleration measured on the rotating surface of the Earth to differ from the acceleration that is measured for a free-falling body: the apparent acceleration in the rotating frame of reference is the total gravity vector minus a small vector toward the north–south axis of the Earth, corresponding to staying ...
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.
For illustration, the first term on the left-hand side is zero for circular orbits, and the applied inwards force equals the centripetal force requirement, as expected. If L is not zero the definition of angular momentum allows a change of independent variable from t {\displaystyle t} to θ {\displaystyle \theta }