Centripetal And Centrifugal Force | Definition, Formulas, Examples.

Centripetal Force

According to Newton's second law of motion, there must be a force acting on a body to produce acceleration. This force must act in the direction of acceleration i.e. along the radius and directed towards the centre of the circle. such a force acting on particle is called centripetal force

Definition - "Force acting on partical performing circular motion, which is along the radius of circle and directed towards the centre of circle."

Since centripetal force acts at right angles to the tangential velocity of particle there is no displacement in the direction of force hence no work is done.

Note

[^r = vector r

 r  = is radius 

m = mass 

v  = linear speed

ω =  angular speed]

As per Newtons Second law of motion 

Force = mass × acceleration 

FCP  = ma 

∵ a = vω = v^2 = rω^2

                     r

∴FCP =   mvω = mv^2  = mrω^2 

                             r

In vector notion,

FCP = -mv^2  ៱r = - mω^2 ^r

               r

S.I. unit = Newton (N)

Important Points, the centripetal force

• is a real force acting on particle performing circular motion
• is a necessary force for maintaining circular motion
• its direction is different at different points 
• acts along the radius of circle and directed towards the centre of circle
• does no work

Examples

1. when a object tied at the end of a string is whirled in a horizontal circle, the necessary centripetal force is maintaining cirular motion is provided by tension in string.
2. in case of a train negotiating the curve, the necessary centripetal force is provided by push due to rails on wheels of a train

 Centrifugal Force (FCF)

Newton's laws of motion valid in a circular motion (accelerated or non-inertial frame of reference) we imagine a pseudo force. Such a pseudo force imagined in circular motion in order to make Newtons laws of motion valid is called a centrifugal force.

Definition - "It is a pseudo force in U.C.M. (Uniform Circular Motion) which acts along radius and directed away from the centre of circle."

FCF = ma 

      = mvω = mv^2 = mrω^2 

                        r

This magnitude is different

In vector form,

FCF = +mv^2 ^r  = + mω^2 ^r

             r

Important Points, the Centrifugal Force 

• pseudo force in U.C.M. is imagined in order to make Newton's laws of motion valid in non-inertial frame of reference.
• acting along the radius, but directed away from the centre of the circle.

   Examples 

1. When a car in motion takes a sudden turn towards left, passenger in car experience an outward push to the right. 
2. A bucket full of water is rotated in vertical circle at a particular speed so the water does not fall 
3. The bulging of earth at equator and flattening at the poles.

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