What is the centripetal force?

Centripetal force is a force that acts on all bodies moving along a circular path. This force is directed towards the center around which the body is moving. This force is associated with the centripetal acceleration (acceleration linked to the change of orientation of the speed vector):  .

Here are some examples of centripetal forces:

• A rotating athletic hammer: the cable exerts a force on the hammer to keep it at a constant distance, it is a centripetal force.
• The movement of the planets: the gravitational attraction exerted by the earth on the moon is a centripetal force. Without this force, the moon would follow a straight path at constant speed.
• A car in a bend: the frictional force between the wheels and the ground is a centripetal force.

The centripetal force is calculated using the following formulas:



Where:

•  is the centripetal force expressed in Newton ()
•  is the body mass expressed in kilograms ()
•  is the radius of the circular path expressed in meters ()
•  is the linear velocity of the body expressed in meters per second ()
•  is the radius of the circular path expressed in meters ()
•  is the angular velocity of the body expressed in radians per second ()

The centripetal force is a real force that acts on a body moving in a circular path and is directed towards the center around which the body is moving.

Calculation based on linear velocity

The centripetal force can be calculated with the following formula:



The general case in vector form is:



Where:

•  is the centripetal force expressed in Newton ()
•  is the body mass expressed in kilograms ()
•  is the linear velocity of the body expressed in meters per second ()
•  is the radius of the circular path expressed in meters ()
•  is a radius vector attached to the center of the circular path, in the direction of the body.

Calculation based on angular velocity

The centripetal force can be calculated with the following formula:



The general case in vector form is:



Where:

•  is the angular velocity of the body expressed in radians per second ()
•  is the angular velocity vector

The centripetal force is a real force that acts on a body moving in a circular path and is directed towards the center around which the body is moving.

Calculation based on linear velocity

The centripetal force can be calculated with the following formula:



The general case in vector form is:



Where:

•  is the centripetal force expressed in Newton ()
•  is the body mass expressed in kilograms ()
•  is the linear velocity of the body expressed in meters per second ()
•  is the radius of the circular path expressed in meters ()
•  is a radius vector attached to the center of the circular path, in the direction of the body.

Calculation based on angular velocity

The centripetal force can be calculated with the following formula:



The general case in vector form is:



Where:

•  is the angular velocity of the body expressed in radians per second ()
•  is the angular velocity vector

The centripetal force is a real force that acts on a body moving in a circular path and is directed towards the center around which the body is moving.

Calculation based on linear velocity

The centripetal force can be calculated with the following formula:



The general case in vector form is:



Where:

•  is the centripetal force expressed in Newton ()
•  is the body mass expressed in kilograms ()
•  is the linear velocity of the body expressed in meters per second ()
•  is the radius of the circular path expressed in meters ()
•  is a radius vector attached to the center of the circular path, in the direction of the body.

Calculation based on angular velocity

The centripetal force can be calculated with the following formula:



The general case in vector form is:



Where:

•  is the angular velocity of the body expressed in radians per second ()
•  is the angular velocity vector

The centripetal force is a real force that acts on a body moving in a circular path and is directed towards the center around which the body is moving.

Calculation based on linear velocity

The centripetal force can be calculated with the following formula:



The general case in vector form is:



Where:

•  is the centripetal force expressed in Newton ()
•  is the body mass expressed in kilograms ()
•  is the linear velocity of the body expressed in meters per second ()
•  is the radius of the circular path expressed in meters ()
•  is a unit vector attached to the center of the circular path, in the direction of the body.

Calculation based on angular velocity

The centripetal force can be calculated with the following formula:



The general case in vector form is:



Where:

•  is the angular velocity of the body expressed in radians per second ()
•  is the angular velocity vector

The centripetal force is a force that acts on a body moving in a circular path and is directed towards the centre around which the body is moving.

Calculation based on linear velocity

The centripetal force can be calculated with the following formula:



The general case in vector form is:



Where:

•  is the centripetal force expressed in Newton ()
•  is the body mass expressed in kilograms ()
•  is the linear velocity of the body expressed in meters per second ()
•  is the radius of the circular path expressed in meters ()
•  is a unit vector attached to the center of the circular path, in the direction of the body.

Calculation based on angular velocity

The centripetal force can be calculated with the following formula:



The general case in vector form is:



Where:

•  is the angular velocity of the body expressed in radians per second ()
•  is the angular velocity vector