Two Secrets of Circular motion

 

Two Secrets of Circular motion

    According to Newton's laws of motion, force is responsible for change in state of rest or state of motion of a body.  If  the force is applied on a body, then body moves in the direction of the applied force in the straight line. To change the direction of motion, it is necessary to change the direction of the applied force.

   First Secret of  Uniform Circular Motion

  The motion of particle along circumference of circle with constant speed is Uniform circular motion ( U.C.M. ) . 

Fig A

Consider a particle of mass m  moving along the circumference of  circle of radius r  (OA ) and tangential velocity V          ( AP ).  For example, the stone is tied to a string and made to revolve in circular path.

 

          To make the stone to move in circular path with O as center , first the stone should be sent in straight path with some velocity V ( AP ), then apply force    ( AO ) on the stone that will be perpendicular to initial velocity by using a string,towards a fixed point. Due to these two vectors,   i. e., the force towards fixed point        ( AO )  and  initial velocity ( AB ) given to stone, the stone will follow resultant path  (AC )  at that instant as per Law of  parallelogram of vectors. Similarly in next position at D Parallelogram ODPQ with resultant DQ is formed. ( Fig B )

                           Fig B 

 

     In this way at every instant the stone will follow resultant motion. Then there is continuous change in path of the stone, but linear velocity and force towards fixed point are continuously present on the stone . Due to all these factors, the path of stone will be along the circumference of the circle. This results into circular motion .

Thus to keep the circular motion two things are necessary:

  1  Tangential or linear velocity V

  2  Applied force,  which is perpendicular to initial velocity

                 ( This is Centripetal force = mV² / r  ).

Second secret of Circular Motion

Centripetal force and Centrifugal force

  To keep the circular motion centripetal force is necessary.  In case of planets revolving around the sun , the gravitational force  supplies the necessary centripetal force. The electrons revolve around the nucleus due to electrostatic force between electron and nucleus which acts as centripetal force.

    The circular motion is an accelerated motion because direction of centripetal force  is continuously changing .  In accelerated  frame of reference Newton's laws are not applicable . Any particle  in circular motion experiences a pseudo force that equals to centripetal force and is opposite to it. This pseudo force is Centrifugal force . This is not a reaction of centripetal force, because both  centripetal force and Centrifugal force act on the same particle in circular motion. Whereas according to Newton's law, action and reaction act on two different bodies .

Thus Centrifugal force is

1 Pseudo force in U.C.M. to make Newton's laws valid.

2 acting along radius, but directed away from center of circle

3 equal to centripetal force  ( = mV² / r ).

   Now consider working of a washing machine drier.  The moisture in wet  cloths contain water which is made to revolve by machine rotation. As there is absence of centripetal force, effect of centrifugal force throws away the water droplets from cloths and thus cloths are dried.

See the videos  to clear the concept of circular motion