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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

centripetal
Directed or moving towards a center.

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.
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.
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 this related concepts: Physics and Other Fields, Damped Harmonic Motion, and Models, Theories, and Laws
 Newton's Second Law
 Appears in this related concepts: Momentum, Force, and Newton's Second Law, Matter Exists in Space and Time, and Momentum Transfer and Radiation Pressure Atom
 acceleration
 Appears in this related concepts: Position, Displacement, Velocity, and Acceleration as Vectors, FreeFalling Objects, and Applications and ProblemSolving
 angular
 Appears in this related concepts: Wavelength, Freqency in Relation to Speed, Bohr Orbits, and Constant Angular Acceleration
 angular acceleration
 Appears in this related concepts: Relationship Between Torque and Angular Acceleration, Angular Acceleration, Alpha, and Conservation of Angular Momentum
 atom
 Appears in this related concepts: Early Ideas about Atoms, The Law of Multiple Proportions, and Stable Isotopes
 axis
 Appears in this related concepts: Area Between Curves, Center of Mass and Translational Motion, and Components of a Vector
 centripetal acceleration
 Appears in this related concepts: Centripetial Acceleration, Simple Harmonic Motion and Uniform Circular Motion, and Accretion Disks
 circular motion
 Appears in this related concepts: Water Waves, XRay Diffraction, and How about relativistic particles?
 equation
 Appears in this related concepts: A General Approach, Equations and Inequalities, and Equations and Their Solutions
 force
 Appears in this related concepts: Driven Oscillations and Resonance, Glancing Collisions, and First Condition
 mass
 Appears in this related concepts: Mass Spectrometer, Mass, and Pop Art
 motion
 Appears in this related concepts: Motion Diagrams, TwoComponent Forces, and Moving Source
 perpendicular
 Appears in this related concepts: The Cross Product, Tangent Vectors and Normal Vectors, and Normal Forces
 radians
 Appears in this related concepts: Rotational Angle and Angular Velocity, Simple harmonic oscillation, and Introduction to the Fourier Series
 rotation
 Appears in this related concepts: Rotational Collisions, Synovial Joint Movements, and Lever Systems
 uniform circular motion
 Appears in this related concepts: Sinusoidal Nature of Simple Harmonic Motion, Kinematics of UCM, and Relationship Between Linear and Rotational Quantitues
 velocity
 Appears in this related concepts: RootMeanSquare Speed, Tangent and Velocity Problems, and Distribution of Molecular Speeds and Collision Frequency
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Cite This Source
Source: Boundless. “Centripetal Force.” Boundless Physics. Boundless, 07 Jan. 2015. Retrieved 21 May. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/uniformcircularmotionandgravitation5/velocityaccelerationandforce53/centripetalforce2584350/