IIT JEE , AIEEE Forum - Physics , Mechanics

sen_holmes

dear sir

Can you please tell me that in circular motion the centrifugal force acts inward or outward?Because in many books the force is taken inwards to solve numerical problems.And in some books the centrifugal force has been taken outwards.I have consulted many books but havent got a satisfactory answer.

astik.pritesh

hi,
sen
look centripetal accln. is directed towards the centre (inwards),
as in the expression for accln. the radial unit vector has a -ve
sign(taking outward +ve).the magn. of this accln. is r*w*w
where w is omega. when multiplied by mass it is called
centripetal force which acts inwards.the centrifugal force has +ve radial u.v. & hence is directed outwards.

ashish040191

centrifugal force acts radially outwards.it acts only in non-inertial frame.centripetal directs 2wards cente.since both have = magnitude ther4, sometimes they r taken same

sen_holmes

thanks a lot guys

sen_holmes

but then how can we understand when to take centrifugal and when to take centripetal for computation??

sudeep.kumar

Well.. a nice doubt where most people get confused...

First, centripetal force...

Any force which provides centripetal acceleration to a body is called a centripetal force.
So, earth is revolving due to the centripetal force.. which is actually gravitational force of sun.. so centripetal force is not a type of force.. it may be gravitational.. may be electrostatic ..etc in nature.. all that it should do is to provide centripetal acceleration.

Now the actual culprit..
All of you must be knowing pseudo force..
When the 'observer' is looking at a body from a non inertial frame (no matter weather the body is at rest, in linear motion, circular motion or whatsoever), then he adds the term of pseudo force so that he could apply newton's 2nd law.. so that he could get sum of all forces, including the pseudo force equal to the mass times the acceleration. Pseudo forces have no existence.. they are mathematical terms used by obsrevers in non inertial frame.

so centrifugal force is a pseudo force.. if we are moving with linear acceleration a, ie the observer is moving with accn a, he adds -ma to all the real forces on anything he observs.
similarly if the observer is rotating with ang vel w, he add the term mw²r in radially outwards direction to use newton's 2nd law.

so if u r rotating with w, but the body is at REST (wtr ground).. at a distance r from the centre of rotation of ur frame (ie centre about which u r rotating), then also u will add mw²r as a virtual force to get mass times accn.

similarly, if u r rotating with w₁ and the body being observed by u is rotating with w_2,then centrifugal force is mw₁²r and not m(w₁-w₂)²r or mw₂²r..etc..

So in summary, if YOU are rotating with w, whatever the body is doing, u must add mw²r to the real forces acting on the body to get ma of the body.. where a is in your frame.. as observed by u.

abhishekgupta

why radially outwards ?since the man is acc towards the center he shud apply the pseudo force on all objects opp to his acc (ie towards the centre ).hence the centgl force must act towards the centre .why shud it act outwards since the outward direction is in the same dir as the man's acc.?

sudeep.kumar

Dear Abhishek, you are just confusing yourself over direction of vectors...

As the man's acceleration is radially inwards, -ma will we in the opposite direction, and that is radially outwards....

because, when we take negative of a vector, its magnitude remains same, and its direction is changed by 180 degree... so opposite of radially inward is radially outwards.

(here centrifugal force is not just -ma... but the actual derivation is for higher classes)

abhishekgupta

thanks sir
for clearing my doubt
ya,it shud act radially outwards .

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