Define centripetal force. Describe the motion of a body in a circular path under the action of centripetal force.

Centripetal Force is the force that acts on an object moving in a circular path, directed towards the center of the circle (or axis of rotation). It is not a new type of force in itself, but rather a result of other forces (such as tension, gravity, or friction) that cause the circular motion.

Characteristics of Circular Motion:

  • A body moving in a circular path constantly changes its direction. This change in direction requires acceleration (called centripetal acceleration), even though the object’s speed may remain constant.
  • The acceleration is always directed towards the center of the circular path, and this is what keeps the object moving in the circle rather than flying off in a straight line (as would happen if no force acted on it).

Centripetal Force Formula:

The formula for centripetal force is:

Fc=mv2/r

Where:

  • Fc = centripetal force,
  • = mass of the object,
  • = velocity of the object in the circular path,
  • = radius of the circular path.

Motion of a Body in Circular Path:

When an object moves in a circular path, its velocity vector is constantly changing direction, even though the object’s speed remains constant. Since velocity is a vector quantity, a change in direction means there is an acceleration. The centripetal force is responsible for this acceleration and directs the object towards the center of the circle.

For example:

  • A car turning around a bend: The friction between the tires and the road provides the centripetal force, allowing the car to follow the curved path.
  • A ball at the end of a string being twirled around in a circle: The tension in the string provides the centripetal force that keeps the ball moving in the circle.

Without centripetal force, an object in circular motion would continue in a straight line due to its inertia.