Centripetal force (from Latin centrum "center" and petere "to seek") is a force that makes a body follow a curved path: its direction is always orthogonal to the velocity of the body, toward the fixed point of the instantaneous center of curvature of the path. Centripetal force is generally the cause of circular motion. In simple terms, centripetal force is defined as a force which keeps a body moving with a uniform speed along a circular path and is directed along the radius towards the centre. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens. Isaac Newton's description was: "A centripetal force is that by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre." Contents [hide] * 1 Formula * 2 Sources of centripetal force * 3 Analysis of several cases * 3.1 Uniform circular motion * 3.1.1 Calculus derivation * 3.1.2 Derivation using vectors * 3.1.3 Example: The banked turn * 3.2 Nonuniform circular motion * 3.3 General planar motion * 3.3.1 Polar coordinates * 3.3.2 Local coordinates * 188.8.131.52 Alternative approach * 184.108.40.206 Example: circular motion * 4 See also * 5 Notes and references * 6 Further reading * 7 External links| -------------------------------------------------
The magnitude of the centripetal force on an object of mass m moving at tangential speed v along a path with radius of curvature r is:
where is the centripetal acceleration. The direction of the force is toward the center of the circle in which the object is moving, or the osculating circle, the circle that best fits the local path of the object, if the path is not circular. The speed in the formula is squared, so twice the speed needs four times the force. The inverse relationship with the radius of curvature shows that half the radial distance requires twice the force. This force is also...