Centripetal and Centrifugal Forces
DEFINITIONS :- 1) Centripetal Force :- a center-seeking force that causes an object to move in a circular path. For example, suppose a ball is tied to a string and swung around in a circle at a constant velocity. The ball moves in a circular path because the string applies a centripetal force to the ball. According to Sir Isaac Newton’s first law of motion, a moving object will travel in a straight path unless acted on by a force. So, if the string were suddenly cut, the ball would no longer be subject to the centripetal force and would travel in a straight line in a direction tangent to the circular path of the ball (if not for the force of gravity). As another example, suppose a person is riding on a merry-go-round. As the merry-go-round rotates, the person must hang onto the ride to keep from falling off. Where the person grasps the ride, a centripetal force is applied to the individual that keeps the person moving in a circular path. If the person were to let go, he or she would travel in a straight line (if gravity were absent). In general, the centripetal force that needs to be applied to an object of mass m that is traveling in a circular path of radius r at a constant velocity v is mv2/r. When a ball is whirled in a circle, it is accelerating inward. This inward acceleration is caused by a centripetal, or center-seeking, force supplied by the tension in the string. The required force is equal to mv2/r, where m is the mass of the ball, v is its velocity (speed and direction), and r is its distance from the center of revolution. 2) Centrifugal Force:- An apparent force that seems to pull a rotating or spinning object away from the centre. Its existence depends upon the frame of reference. As it is a pseudo force, obviously it comes into play only when the viewer is in a non - inertial frame. THE MISCONCEPT :- Often, centripetal force is confused with centrifugal force. While centripetal force is a real force,—that is, the force is due to the influence of some object or field—centrifugal force is a fictitious force. A fictitious force is present only when a system is examined from an accelerating frame of reference. If the same system is examined from a non-accelerating frame of reference, all the fictitious forces disappear. For example, a person ( viewer himself ) on a rotating merry-go-round would experience a centrifugal force that pulls away from the center of the ride. The person experiences this force only because he or she is on the rotating merry-go-round, which is an accelerating frame of reference. If the same system is analyzed from the sidewalk next to the merry-go-round, which is a non-accelerating frame of reference, there is no centrifugal force. The individual on the sidewalk would only note the centripetal force that keeps the individual moving in a circular path. In general, real forces are present regardless of whether the reference frame used is accelerating or not accelerating; fictitious forces are present only in an accelerating frame of reference. THE WRONG ASSUMPTION :- Thats not right !!! C.p. force is not a new type of force acting on the body undergoing circular motion. When a body undergoes circular motion, a force ( one among the four forces of nature, e.g. gravitational, electrostatic, magnetic etc, etc ) always acts on the body perpendicular to its motion. That force has a magnitude of its own (according to the law which defines that force) and that magnitude is just equal to mv2/r. Thats it. But when anyone observes the circular motion from any non-inertial frame, the accl^n of the body w.r.t that frame = {vct(F) - vct(f)} / m. where vct(f) = pseudo force = centrifugal force = m x accln of. the non inertial frame of reference. and vct(F) = force acting on the body as seen from inertial frame = m x accln w.r.t inertial frame = force which causes circular motion ( Force perp. to velocity) which acts as c.p. force ( = mv2/r) in case of inertial frame. Now if accln of the body w.r.t the non - inertial frame = 0 then, vct(F) = vct(f) => magnitude of Force causing circular motion = magnitude of c.f. force. this is the case when the body appears to be at rest.. NOTE:- here we are not writing the force causing circular motion as c.p. force, as we will not be observing the body to go in a circle (which is possible only if we are observing the motion from an inertial frame). So c.p. force and c.f. force can never act together on a body.
Now what some people do is that, they say the body remains in its place while going in circular motion because c.p. force and c.f. force cancel each other.