# Centrifugal and centripetal

hey guys,

I know this topic has been discussed before, but I have a stupid question about it: we know that in circular motion we always have an acceleration towards the center (centripetal acceleration) but we also have a force that points radially outwards (centrifugal force). Some text books said that this is a fictitious force, but my question is that we always feel that force (for example if you're sitting in a car as it goes around a turn, you'll feel a force pushing you in the opposite direction) so it is not a fictitious force, and also how come this force is pointing opposite of the acceleration? according to Newton's second law, you'd expect the force to point along acceleration ?

I'd apperciate your replies..Thanks a lot.

DaveC426913
Gold Member
Moneer81 said:
...a force that points radially outwards (centrifugal force). Some text books said that this is a fictitious force, but my question is that we always feel that force (for example if you're sitting in a car as it goes around a turn, you'll feel a force pushing you in the opposite direction)

The force does not point outward, despite the fact that it seems to. If you are going round a merry go round, and suddenly let go, you do not go flying outward from the merry-go-round (much as it seems you do). You actually go flying tangential to the merry-go-round at the point where you let go.

There is no force throwing you off the merry-go-round, there is only your inertia that carries you in a straight line.

For this reason, even though, subjectively, it seems you have a force acting on you, it is an illusion.

Juicy Jon
moneer,

Actually the force you "feel" when the car goes around a corner is the force the car exerts on you to change your momentum and make you go around the corner with it. If the car turns left it pushes on your right side causing you to accelerate to the left with the car. That's centripetal force.

If there were really an equal centrifugal force pushing you the other way, the two would cancel, and you would keep going in a straight line instead of going around the corner with the car

Dave is right. A body that hass mass has a propery of inertia. It has a resistance to change in direction or speed. This is why when you turn a corner in your car, the centripital force is not actually pushing you out from the centre of the circe, it is your body which has an inertia to go in the same direction that causes this force when the car turns. This why you feel a force on yourself.
Also, jdavel is right, the force is tangental to the radius of the circle, not radial.

DaveC426913 said:
The force does not point outward,

The centrifugal force DOES point outward but you go flying off in the tangential direction because the velocity is always tangential to the circle. The direction of a force is NOT equal to the direction in which you move in this case.

Here is another example. Suppose you have two observers. One inertial observer that stands still at the centre of some big circle of radius R. A second (non-inertial) observer moves around on the circle. The reason why this observer is not inertial is because his frame reference has no constant velocity and there is a force working on it. This is the centripetal force that makes it go around the circle. Suppose the moving observer carries a spring with him and he wants to describe it.

The inertial observer will write mv²/R = -kx for the second law of Newton (he sees the spring moving on a circle).
The non-inertial observer sees a spring that stands still with respect to his frame. So he wants to write $$ma_{non-inertial}$$ = -kx. But however this is incorrect and it will not correspond to the measurements he makes (-kx will not be obeyed by the spring due to the circular motion). In order to correct his measurements he will have to write $$ma_{non-inertial}$$ = -kx -mv²/R and the latter is the centrifugal force. This force is a pseudo-force because it is a consequence of his rotation and it basically has nothing to do with the spring, only with the fact that his frame moves.

generally it will be that for some force F $$a_{non-inertial} = a_{inertial}-a_{0}$$ where the $$a_{0}$$ is the acceleration of the non inertial frame with respect to the inertial frame and $$a_{inertial}$$ is the acceleration of the force F, which is in this case the acceleration of the spring. If you multiply all of this with mass you get forces. Keep in mind that in this example the spring really works on the non-inertial observer

regards
marlon

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Juicy Jon
Centripedal acceleration is mathematically consistent with newtonian mechanics. Centrifugal force is not.

Proof: Suppose a bucket you swing around feels a centrifugal force. Than, surely it feels a center seeking force as well (from the handle). Then, since the forces pseudo-cancel, the object is not accelerating.

But its velocity is changing! Glaring inconsistency.

dextercioby
Homework Helper
1.Marlon mistyped 2ice the expression for centripetal force.To him,(kinetic) energy and force are the same things dimensionally so they can be added.
Let's take is an inherent error...But Twice??? :tongue2:

2.However,Marlon did make a point...It's probably because to him and I noninertial reference frames & forces are not an enigma in Newtonian mechanics and if they were,we would have not made anything out of GR.

I advice you all to take a look into both Marlon's post and a mechanics book before opening your mouth and fingers on noninertial forces and reference frames.Obviously you are all (except Marlon,obviously) missinformed.The bad part is that u induce the same amount of error into innocent persons...

Daniel.

Juicy Jon
dextercioby
Homework Helper
Marlon,i hope you don't mind yet another irony.After all,u do the same thing with me... :tongue2: So we're even,just like centripetal and centrifugal forces in noninertial reference frames... :tongue2:

Daniel.

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Indeed dexter, i have corrected it in my original post.

Thanks for pointing that out to me

regards
marlon

wow ...

this forum rocks...thanks guys for all your informative replies.

dextercioby
Homework Helper
Moneer81 said:
wow ...

this forum rocks...thanks guys for all your informative replies.

Let's hope you're thanking Marlon and I...The other replies you can throw outta window...

Daniel.

rcgldr
Homework Helper
Centripetal force is a force that causes an moving object to follow a circular path. This results in an inwards acceleration that corresponds with a "reactive" outwards centrifugal force. If you're in one of those amusement park spinning drums, the walls of the drum push your body inwards to follow a circular path, and the acceleration on your body results in the reactive force that you body exerts back on the wall.

I had a discussion a/b this with dextercioby here and finally reached basically the same conclusion as he and marlon. Post #6 sums it up nicely I think.

dextercioby