Centripetal force is the force that acts on an object moving in a circular path, always directed toward the center of the circle. It is responsible for keeping the object in its curved path, continuously changing its direction but not its speed.
Centripetal force is always directed perpendicular to the direction of motion of the body because it acts to change the object's direction, not its speed. The force acts inward, toward the center of the circle, as the object tries to move in a straight line but is continuously forced to curve.
According to Newton's second law of motion, the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
F_net = m * a
In the case of circular motion, the acceleration is directed toward the center of the circle. This centripetal acceleration (a_c) is given by the equation:
a_c = v^2 / r
where v is the velocity of the object and r is the radius of the circular path.
To maintain this acceleration, a centripetal force (F_c) is required, and it is given by:
F_c = m * a_c
Substituting the expression for centripetal acceleration, we get:
F_c = m * (v^2 / r)
This force acts in the direction toward the center of the circle, perpendicular to the velocity of the object. It continually changes the direction of the object's motion, preventing it from moving in a straight line and keeping it in the circular path.