Centripetal force
Centripetal force
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Not to be confused with Centrifugal force.
This article contains many unreferenced sections and needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2011)
Roller coaster cars are forced through a loop by the track applying a centripetal force on them. A reactive centrifugal force is applied to the track by the cars.
Centripetal force (from Latin centrum "center" and petere "to seek"[1]) 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.[2][3] 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."[4]
Contents
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
3.3.2.1 Alternative approach
3.3.2.2 Example: circular motion
4 See also
5 Notes and references
6 Further reading
7 External links
Formula
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:[5]
where is the centripetal acceleration. The direction of the force is toward the center of the
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Not to be confused with Centrifugal force.
This article contains many unreferenced sections and needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2011)
Roller coaster cars are forced through a loop by the track applying a centripetal force on them. A reactive centrifugal force is applied to the track by the cars.
Centripetal force (from Latin centrum "center" and petere "to seek"[1]) 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.[2][3] 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."[4]
Contents
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
3.3.2.1 Alternative approach
3.3.2.2 Example: circular motion
4 See also
5 Notes and references
6 Further reading
7 External links
Formula
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:[5]
where is the centripetal acceleration. The direction of the force is toward the center of the