Centripetal force is the force that pushes an object towards the center of a circle as it moves in a circular motion. It is the force acting on an object moving in a circle, directed towards the center of the trajectory.

The centripetal force is a force acting on all bodies moving along a circular trajectory. This force is directed in the direction of the trajectory's center of rotation. It is the force that keeps an object in motion on a circular trajectory by constantly directing it towards the center of this trajectory. It is responsible for the object's change of direction and acts perpendicular to the object's speed, pointing towards the center of the circle around which the object is moving.

Characteristics of the centripetal force:

• Direction: It is always directed towards the center of the circular path.
• Nature: It can be generated by a variety of forces, depending on the context, such as string tension, gravity, friction or electromagnetic force.
• Effect: It does not change the object's speed (i.e. the intensity of its velocity), but it does alter its direction, resulting in circular motion.

Formula for centripetal force :

The centripetal force $F_c$ is given by the formula:
$$F_c = \dfrac{m v^2}{r} = mr\omega^2$$

• $\vec{F_c}$ is the centripetal force expressed in Newton ( $N$ )
• $m$ is the mass of the object expressed in kilograms ( $kg$ )
• $\vec{v}$is the linear velocity tangent to the trajectory expressed in meters per second ( $m.s^{-1}$ )
• $r$ is the radius of the circular path expressed in meters ( $m$ )
• $\omega$ is the angular velocity of the body expressed in radians per second ( $rad.s^{-1}$ )

Examples:

• A satellite orbiting the Earth : Gravity provides the centripetal force that keeps the satellite in orbit.
• An athletics hammer in rotation: The cable exerts a force on the hammer to keep it at a constant distance; this is a centripetal force.
• A vehicle on a bend : The friction between the tires and the road provides the centripetal force that enables the vehicle to follow the bend.

Thus, the centripetal force is essential to maintain any object in circular motion, acting as a force that “pulls” the object towards the center of rotation.