# 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).

#### 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

• Directed or moving towards a center.

• 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.

#### Figures

1. ##### Centripetal force

As an object travels around a circular path at a constant speed, it experiences a centripetal force accelerating it toward the center.

2. ##### Centripetal Force

A brief overview of centripetal force.

A force that causes motion in a curved path is called a centripetal force Figure 2. 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 Figure 1. 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:

$F_c = mv^2/r$, where: Fc = centripetal force, m = mass, v = velocity, and r = radius of path of motion.

Looking back to the atom on Newton's Second Law - Acceleration, we can see that centripetal acceleration is:

$a_c = v^2/r$.

We also know that the equation for Force is: $F = m*a$. From this, we can figure out that the equation for centripetal force is: $F_c = mv^2/r$, where: Fc = centripetal force, m = mass, v = velocity, and r = radius of path of motion.

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:

$F_c = mr\omega^2$

#### Key Term Glossary

acceleration
The amount by which a speed or velocity increases (and so a scalar quantity or a vector quantity).
##### Appears in these related concepts:
Acceleration
the rate at which the velocity of a body changes with time
##### Appears in these related concepts:
angular
Relating to an angle or angles; having an angle or angles; forming an angle or corner; sharp-cornered; pointed; as in, an angular figure.
##### Appears in these related concepts:
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.
##### Appears in these related concepts:
atom
The smallest possible amount of matter which still retains its identity as a chemical element, now known to consist of a nucleus surrounded by electrons.
##### Appears in these related concepts:
axis
An imaginary line around which an object spins (an axis of rotation) or is symmetrically arranged (an axis of symmetry).
##### Appears in these related concepts:
centripetal
Directed or moving towards a center.
##### Appears in these related concepts:
centripetal acceleration
Acceleration that makes a body follow a curved path: it is always perpendicular to the velocity of a body and directed towards the center of curvature of the path.
##### Appears in these related concepts:
circular motion
Motion in such a way that the path taken is that of a circle.
##### Appears in these related concepts:
equation
An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity.
##### Appears in these related concepts:
force
A physical quantity that denotes ability to push, pull, twist or accelerate a body which is measured in a unit dimensioned in mass × distance/time² (ML/T²): SI: newton (N); CGS: dyne (dyn)
##### Appears in these related concepts:
Force
A force is any influence that causes an object to undergo a certain change, either concerning its movement, direction or geometrical construction.
##### Appears in these related concepts:
Law
A concise description, usually in the form of a mathematical equation, used to describe a pattern in nature
##### Appears in these related concepts:
mass
The quantity of matter which a body contains, irrespective of its bulk or volume. It is one of four fundamental properties of matter. It is measured in kilograms in the SI system of measurement.
##### Appears in these related concepts:
motion
A change of position with respect to time.
##### Appears in these related concepts:
perpendicular
at or forming a right angle (to).
##### Appears in these related concepts:
The angle subtended at the centre of a circle by an arc of the circle of the same length as the circle's radius.
##### Appears in these related concepts:
rotation
The act of turning around a centre or an axis.
##### Appears in these related concepts:
tension
Force transmitted through a rope, string, cable, or similar object (used with prepositions on, in, or of, e.g., "The tension in the cable is 1000 N", to convey that the same magnitude of force applies to objects attached to both ends).
##### Appears in these related concepts:
uniform circular motion
Movement around a circular path with constant speed.
##### Appears in these related concepts:
velocity
A vector quantity that denotes the rate of change of position with respect to time, or a speed with a directional component.
##### Appears in these related concepts:
Velocity
The rate of change of displacement with respect to change in time.