Centripetal force is a fundamental concept in physics that explains why objects move in circular paths. It is the force acting on a body moving in a circular path, directed towards the center around which the object moves. This inward force ensures that the object remains on its curved trajectory rather than continuing in a straight line.

Formula

As with any other force, the centripetal force follows Newton’s Second Law:

\[ F_C = m \cdot a_c \]

• \( F_C \): centripetal force
• \( m \): mass of the object
• \( a_c \): centripetal acceleration of the object

Centripetal acceleration is defined by the following formula:

\[ a_c = \frac{v^2}{R} = \omega^2 \cdot R \]

• \( v \): velocity of the object¹
• \( R \): radius of the circular path
• \( \omega \): angular velocity of the object

¹Usually the tangential velocity of the object, except in some problems that involve rolling with sliding.

Examples of Centripetal Force

• The tension in the rope on a tetherball serves as the centripetal force keeping the ball in circular motion around the pole.

• Friction between both wheels and the floor provides the necessary centripetal force for a biker to turn in circles.

• The gravitational pull of Earth on the Moon acts as the centripetal force maintaining the Moon's orbit around Earth.

Written by Mateo Sancho