Define centripetal force.

Centripetal force is the force that keeps an object moving in a circular path.

Centripetal force, from the Latin words 'centrum' meaning 'centre' and 'petere' meaning 'to seek', is a fundamental concept in physics. It is the force that acts on an object moving in a circular path and is always directed towards the centre of the path. This force is necessary to keep an object moving along a circular path, as it continuously changes the object's direction of motion.

The magnitude of the centripetal force on an object of mass m moving at a speed v along a path with radius r is given by the formula F = mv²/r. This formula shows that the centripetal force increases with the square of the speed, meaning that if the speed is doubled, the centripetal force increases by a factor of four. Similarly, the centripetal force is inversely proportional to the radius of the path, meaning that if the radius is doubled, the centripetal force is halved.

Centripetal force can be provided by various forces depending on the situation. For example, in the case of a planet orbiting a star, the centripetal force is provided by the gravitational force between the planet and the star. In the case of a car taking a turn, the centripetal force is provided by the frictional force between the car's tyres and the road.

It's important to note that centripetal force is not a new kind of force, but rather a role that other forces can play. It's also worth mentioning that there's a common misconception about a 'centrifugal' force acting outwards from the centre of the circle. This is a fictitious force that only appears to exist in a rotating frame of reference. In reality, it's the centripetal force that's keeping the object in circular motion.

Understanding centripetal force is crucial in physics as it helps explain phenomena such as the orbits of planets, the operation of centrifuges, and the dynamics of cars taking turns. It's a key concept in the study of circular motion and rotational dynamics.