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 Objective

Express the equations for the centripetal force and 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.
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. 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:
where:
From Newton's second law
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: Physics and Other Fields, Damped Harmonic Motion, and Models, Theories, and Laws
 Newton's Second Law
 Appears in these 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 these related concepts: Position, Displacement, Velocity, and Acceleration as Vectors, Scientific Applications of Quadratic Functions, and The Second Law: Force and Acceleration
 angular
 Appears in these related concepts: Wavelength, Freqency in Relation to Speed, Bohr Orbits, and Constant Angular Acceleration
 angular acceleration
 Appears in these related concepts: Relationship Between Torque and Angular Acceleration, Angular Acceleration, Alpha, and Conservation of Angular Momentum
 axis
 Appears in these related concepts: Area Between Curves, Regional Terms and Axes, and Components of a Vector
 centripetal acceleration
 Appears in these related concepts: Kinematics of UCM, Simple Harmonic Motion and Uniform Circular Motion, and Centripetial Acceleration
 circular motion
 Appears in these related concepts: Water Waves, B.3 Chapter 3, and XRay Diffraction
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 force
 Appears in these related concepts: Force of Muscle Contraction, Force, and First Condition
 mass
 Appears in these related concepts: Mass Spectrometer, Pop Art, and Mass
 motion
 Appears in these related concepts: Motion Diagrams, TwoComponent Forces, and Moving Source
 perpendicular
 Appears in these related concepts: The Cross Product, Tangent Vectors and Normal Vectors, and Circular Motion
 radians
 Appears in these related concepts: Thin Film Interference, Rotational Angle and Angular Velocity, and Position, Velocity, and Acceleration as a Function of Time
 rotation
 Appears in these related concepts: Rotational Collisions, Lever Systems, and Transformations of Functions
 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: Velocity of Blood Flow, RootMeanSquare Speed, and Rolling Without Slipping
Sources
Boundless vets and curates highquality, openly licensed content from around the Internet. This particular resource used the following sources: