1. Circular Motion & Gravition
Chapter 7
Circular Motion & Gravition

2. 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.

3. 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’ .

4. 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 or 

5. 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.

6. 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.

7. 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

8. 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”

9. 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"