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Centripetal Force
A force which causes motion in a curved path is called a centripetal force (uniform circular motion is an example of centripetal force).
Learning Objectives

Express the equation for the centripetal force

Express the equation for the centripetal acceleration
Key Points
 When an object is in uniform circular motion, it is constantly changing direction, and therefore accelerating. This is angular acceleration.
 A force acting on the object in uniform circular motion (called centripetal force) is acting on the object from the center of the circle.
 Centripetal Force is given by .
Terms

angular velocity
A vector quantity describing an object in circular motion; its magnitude is equal to the speed of the particle and the direction is perpendicular to the plane of its circular motion.

centripetal
Directed or moving towards a center.
Full Text
A force that causes motion in a curved path is called a centripetal force . Uniform circular motion is an example of centripetal force in action. It can be seen in the orbit of satellites around the earth, the tension in a rope in a game of tether ball, a roller coaster loop de loop, or in a bucket swung around the body.
Previously, we learned that any change in a velocity is an acceleration. As the object moves through the circular path it is constantly changing direction, and therefore accelerating—causing constant force to be acting on the object. This centripetal force acts toward the center of curvature, toward the axis of rotation, as seen in . Because the object is moving perpendicular to the force, the path followed by the object is a circular one. It is this force that keeps a ball from falling out of a bucket if you swing it in circular continuously.
Centripetal force
As an object travels around a circular path at a constant speed, it experiences a centripetal force accelerating it toward the center.
The equation for centripetal force is as follows:
Looking back to the atom on Newton's Second Law  Acceleration, we can see that centripetal acceleration is:
We also know that the equation for Force is:
Centripetal force can also be expressed in terms of angular velocity. Angular velocity is the measure of how fast an object is traversing the circular path. As the object travels its path, it sweeps out an arc that can be measured in degrees or radians. The equation for centripetal force using angular velocity is:
Key Term Reference
 Law
 Appears in these related concepts: Mechanical Work and Electrical Energy, Gauss's Law, and Models, Theories, and Laws
 Newton's Second Law
 Appears in these related concepts: Driven Oscillations and Resonance, Momentum, Force, and Newton's Second Law, and Matter Exists in Space and Time
 acceleration
 Appears in these related concepts: Position, Displacement, Velocity, and Acceleration as Vectors, Graphical Interpretation, and The Second Law: Force and Acceleration
 angular
 Appears in these related concepts: Wavelength, Freqency in Relation to Speed, Rotational Collisions, and Constant Angular Acceleration
 angular acceleration
 Appears in these related concepts: Torque, Relationship Between Torque and Angular Acceleration, and Angular Acceleration, Alpha
 atom
 Appears in these related concepts: The Law of Multiple Proportions, Stable Isotopes, and John Dalton and Atomic Theory
 axis
 Appears in these related concepts: Adding and Subtracting Vectors Graphically, Area Between Curves, and Components of a Vector
 centripetal acceleration
 Appears in these related concepts: Centripetial Acceleration, Kinematics of UCM, and Simple Harmonic Motion and Uniform Circular Motion
 circular motion
 Appears in these related concepts: Water Waves, XRay Diffraction, and Angular vs. Linear Quantities
 equation
 Appears in these related concepts: A General Approach, Equations and Inequalities, and Equations and Their Solutions
 force
 Appears in these related concepts: Work, Force, and Force of Muscle Contraction
 mass
 Appears in these related concepts: Mass Spectrometer, Mass, and Pop Art
 motion
 Appears in these related concepts: Motion with Constant Acceleration, Newton and His Laws, and Motion Diagrams
 perpendicular
 Appears in these related concepts: The Cross Product, Circular Motion, and Normal Forces
 radians
 Appears in these related concepts: Position, Velocity, and Acceleration as a Function of Time, Period and Frequency, and Rotational Angle and Angular Velocity
 rotation
 Appears in these related concepts: Synovial Joint Movements, Lever Systems, and Rotational Kinetic Energy: Work, Energy, and Power
 uniform circular motion
 Appears in these related concepts: Sinusoidal Nature of Simple Harmonic Motion, Circular Motion, and Relationship Between Linear and Rotational Quantitues
 velocity
 Appears in these related concepts: Rolling Without Slipping, RootMeanSquare Speed, and Applications and ProblemSolving
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Cite This Source
Source: Boundless. “Centripetal Force.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 04 Oct. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/uniformcircularmotionandgravitation5/velocityaccelerationandforce53/centripetalforce2584350/