Circular Motion & Gravition Chapter 7 Circular Motion & Gravition

CIRCULAR MOTION AND GRAVITATION  Every object in our universe attracts the other object with certain fore towards its center. This force of  attraction is known as GRAVITATIONAL FORCE and the phenomenon is called GRAVITATION. This is  gravitational force which is responsible for the uniformity or regularity in our daily astronomical life. The  whole system of the universe is in order only due to this force. Due to gravitation, the system of our  universe is working uniformly and smoothly. The planets around the earth or around the sun moves in an  orderly motion due to gravitation.

NEWTON’S LAW OF GRAVITATION  In order to explain the gravitational force between two bodies, Newton formulated a fundamental law known after his name i.e. "NEWTON'S LAW OF GRAVITATION" Newton’s law of gravitation states that every object in the universe attracts the other object with a force and :  (1) The gravitational force of attraction between two bodies is directly proportional to the product of their  masses. F a m1 x m2 ------- (1)  (2) The gravitational force of attraction between two bodies is inversely proportional to the square of the  distance between their centers. F a 1/d2 --------- (2) MATHEMATICAL REPRESENTATION  Combining (1) and (2) F a m1m2 /d2 F = G m1m2/d2  Where G = universal gravitational constant  Value of G:  G = 6.67 x 10-11 Nm2/kg2 MASS OF THE EARTH  Consider a body of mass ‘m’ placed on the surface of the earth. Let the mass of the earth is ‘Me’ and  radius  of earth is ‘Re’ .

F = G m Me/ Re2 F = W W = G m Me/ Re2 mg = G m Me/ Re2 or g = G Me/Re2  Gravitational force of attraction between earth and body is F = G m Me/ Re2  We know that the force of attraction of the earth on a body is equal to weight the weight of body.  i.e F = W  Therefore W = G m Me/ Re2  But W = mg mg = G m Me/ Re2 or g = G Me/Re2 or Me = g x Re2/G  From astronomical data:  g= 9.8 m/s2  Re = 6.4 x 106 m  G = 6.67 x 10-11 N-m2/kg2  Putting these values in the above equation. Me = 9.8 (6.4 x 106)2/6.67 x 10-11 or 

CENTRIPETAL FORCE-CENTRIFUGAL FORCE-CENTRIPETAL ACCELERATION Centripetal force is defined as the force necessary to move a body in a circular path and is always directed towards the centre of the circular path. OR When a body moves in a circular path with uniform velocity, it experiences a force,  directed along the radius towards the centre of the circle. This force is called CENTRIPETAL FORCE.

MATHEMATICAL REPRESENTATION  Centripetal force depends upon the mass of body, velocity of body and the radius of circular path. CENTRIFUGAL FORCE  When a body of moves around circle, centripetal force acts upon it. According Newton’s third law of motion  another force equal to centripetal force but opposite in direction also acts upon it . This force is referred to  as CENTRIFUGAL FORCE.

Mathematical The force acting in the opposite direction of centripetal force is called centrifugal force. Action Force = Centripetal Force Reaction Force = Centrifugal Force. According to Newton’s 3rd Law of motion Action Force = -Reaction Force Where negative sign shows the opposite direction. Centripetal Force = Centripetal Force

CENTRIPETAL ACCELERATION When a body moves around a circle with constant speed, the direction of its velocity continuously changes.  Due to change in direction, its velocity changes. A changing velocity imparts an acceleration in the body.  The direction of this acceleration is always towards the centre of circle. This acceleration i        According to 2nd law of motion Fc = mac ..........(1) but  Fc = mv2 / r ........(2) From (1) and (2) we get mac = mv2 /r or ac = v2/r   Where ac = centripetal acceleration, V2 = speed of the moving object, r = radius of the circular orbit. Its unit is m/s2. s known as  "CENTRIPETAL acceleration”

UNIFORM CIRCULAR MOTION  If a body moves in a circular path with constant speed or uniform speed then the motion of the body is said  to be "uniform circular motion"