Kinematics of Circular Motion:
If an object moves in a circular path with constant speed, its motion is called uniform circular motion.The line perpendicular to plane of motion of the body about which the body rotates is called axis of rotation.The line joining the instantaneous position of the body and centre of the circle is called radius vector.The angle swept by the radius vector in a given interval of time is called angular displacement q. S.I unit of q is radian.Angular velocity 'w' of an object in circular motion is defined as the time rate of change of its angular displacement 
= d
/dt S.I. unit is rad s-1
It is an avail vector.
Angular acceleration 
of an object in circular motion is defined as the time rate of change of its angular velocity = d/dt SI unit is rad s-2.
The acceleration possessed by a body moving in a circular path and directed towards the centre is called centripetal or radial acceleration.a = v2/r = r
2, (in m/s2 ) where v and are the linear velocity, angular velocity of the body and 'r' radius of the circleCentripetal Force :
The force required to keep the body in circular path is centripetal force.
The centripetal force changes the direction of the velocity but not the magnitude of the velocity. It acts perpendicular to the direction of motion of the body.Note : The gravitational force of attraction provides the necessary centripetal force for the moon to go round the earth.
Centrifugal Force :
The accelerated frame of reference is the frame of reference which is moving with an acceleration.When a body revolving round in a circular path is in the accelerated frame of reference, it is observed that the body is experiencing a centrifugal force.The magnitude of centrifugal force is equal to the centripetal force. The centrifugal force acts away from the centre.Banking Of Roads And Railway Tracks :
The roads and rail roads are banked to provide the necessary centripetal force from the normal reaction.Centripetal force = horizontal component of normal reaction = N sin
Centripetal force = Resultant of the normal reaction and weight =
The angle of banking is given by 
where 'v' is the velocity of the vehicle on the road of radius 'r'.The maximum velocity for a vehicle on a banked road is
.motion in a vertical circle :
A particle of mass 'm' suspended by a thread is given a horizontal speed 'u', when it is at 'A', it moves in a vertical circle of radius 'r'When the angular displacement of the particle is '', ie when the particle is at pSpeed of the particle v = 
where u is the velocity at A, the lowest point Centripetal force mv2/r = T - mg cos Tangential acceleration = g sin Tangential force = mg sin Tension in the string T = mv2/r + mg Cos 
Tensions at lowest point (i.e, = 0) is given by T = (mv2/r) + mg and is maximum.Where V is the velocity at the lowest point.
Tension at the highest point (i.e, = 180o) is T = (mv2/r) - mg and is minimum where 'V' is the velocity at highest pointThe minimum velocity at the lowest point to just complete the circle is 
WHEN A BODY IS ROTATED IN A HORIZONTAL CIRCLE :
The body can be rotated with uniform speed or non-uniform speed.
When the body is moving round with uniform speed
i) It has centripetal force of constant magnitude equal to
.ii) It has tension of constant magnitude
iii) Its KE remains constant.
iv) It has centripetal acceleration of constant magnitude
or 
.
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