Centripital force
The force which keeps the body to move in a circular path is called centripital force.
OR
The force which bend the normally straight path in to circular path in known as centripital force.
It is denoted by Fc . its formula is
Fc = mv2/r
Centripital accelration
If an object is moving in a circle with constant speed, then direction of its motion is continuously changing. Due to change in direction of body an acceleration is produced in the object The directionof acceleration is towards the center of circle. This acceleration is called is called "centripetal acceleration".
It is denoted by ac.
Expression For Fc
Suppose a body is moving in a circle of radius r with constant speed V. Let it travels from point A to B
in a time interval of Dt sec and covers a distance DS meter. Let velocity vector of the body at point
A be V1 and at point B be V2.Angle traced at the center during this interval Dt sec is say Dq .
Take a point O outside circle, draw velocity vector OP and OQ equal and parallel to V1 and V2. Join PQ from vector addition head and tail rule OQ i.e. V2 is resultant of OP = V1 and PQ = DV. It means PQ is the change in velocity DV during interval Dt sec.
in a time interval of Dt sec and covers a distance DS meter. Let velocity vector of the body at point
A be V1 and at point B be V2.Angle traced at the center during this interval Dt sec is say Dq .
Take a point O outside circle, draw velocity vector OP and OQ equal and parallel to V1 and V2. Join PQ from vector addition head and tail rule OQ i.e. V2 is resultant of OP = V1 and PQ = DV. It means PQ is the change in velocity DV during interval Dt sec.
DV = V2 – V1
Angle POQ is equal to angle at the center of circle becomes V1 and V2 are perpendicular to radius lines at A and B. From geometry DACB and DOPQ are similar because both are in closed triangles and Dq are same.
By similer properties
D V / V = D S / r
D V = V. D S/r
Dividing both sides by D t
D V / D t = V/r . D S/D t
When Dt is very small D tè 0
D V / D t is lim DV / Dt
D tè 0
V / r lim DS / Dt
D tè 0
ac = V / r * V
ac = V2 / rThis is the magnitude of centripital accelration.
By 2nd law of motion
Fc = ma
Fc = m(v2/r)
Fc = mv2/r
In angular motion
V =rω
Therefore
Fc = mr2ω2/r
Fc = mrω2
(www.pak-physicsnotes.blogspot.com)
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