UNIFORM CIRCULAR MOTION

UNIFORM CIRCULAR MOTION

               When an object moves at a constant speed in a straight line both the magnitude and direction of velocity vector remains unchanged, however, if a force is acting on the body (object) in the direction of its motion and the magnitude of velocity (speed) changes but the direction of velocity remain same and acceleration produced in the direction of motion. If force is acting perpendicularly to the direction of motion, then magnitude of velocity (speed) remains the same but its direction changes at every point. It means there is change in velocity. There must be some acceleration and object due to this force moves in curve path. The simplest type of curve path is circle.

               “When a body moves in a circular path with constantly speed it is said to describe uniform circular motion.”

CENTRIPETAL ACCELERATION

               Consider a body of mass “m” moving with constant speed “v” around circle of radius “r”. At any instant the direction of velocity is directed along the tangent to the circular path. As the body moves along the circumference of the circle the direction of velocity is continuously changing, it has acceleration. According to Newton’s law of motion a force must be acting upon it. If the magnitude of velocity (speed) remain constant this force must be at right angle to the tangent to the circle, and it is directed towards the centre of the circle called centripetal force(force directed towards the centre). According to the Newton’s second law of motion, the centripetal force produces acceleration on its own direction called centripetal acceleration. It can be shown that the magnitude of centripetal acceleration is equal to square of the speed divided by the radius of circle. The magnitude of this acceleration “   “is given by

                                                                                      mv^2

                                            Centripetal acceleration= -------

                                                                                          r

CENTRIPETAL FORCE

“The force which acts towards the centre along the radius of a circular path on which the body moving with a uniform velocity is called a centripetal force.”

               From Newton Second law of Motion, we have

                              F=ma_c

Where “a_c “is the centripetal acceleration produced by centripetal force “F”. Substituting the value of     in above equation, we have centripetal force

Thus the centripetal force is directly proportional to the mass of the object, to the square of its linear speed and inversely proportional to the radius of circular path.

CENTRIFUGAL FORCE

               When a body moving along circular path it has a tendency to move along the tangent but a force is acting on it directed towards the centre of circle which keeps the body to move in circle called centripetal force. According to Newton’s third law of motion, there must be a reaction force directed away from the centre of circle and is equal in magnitude but opposite to centripetal force called centrifugal force.

               When a stone at the end of a string whirl, to keep the stone in circular motion a force act pulls it inward along the string. According to third law of motion stone reacts and exert an equal force outward on the hand. The outward force on the hand is called centrifugal force.