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While learning Classical Mechanics, I am confused on nature and application of centrifugal force.

In my textbook, it is written that centrifugal force is a pseudo force that, depends on reference frame, but I can't understand that if it is pseudo force then why we feel something pushing us outwards during a tight turn in vehicle.

Also, I am very confused that when we will apply centrifugal force, since centrifugal will cancel centripetal force so how will the object move in circle in absence of radial acceleration? (My understanding)

Please clarify my confusion and tell any flaws in my understanding if any,

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    $\begingroup$ It is also called fiticious force, or d'Alembert force, or inertial force. I prefer the term inertial force, because we do feel it, not an imagination. $\endgroup$ – ytlu Jan 24 at 16:27
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    $\begingroup$ It is a reference frame problem. Your body is moving in a straight line and resists change (Newton's first law). The car changes direction and thus is pushing the car seat, door etc into your body. Your brain interprets this pushing of the entire car into your body as you experiencing a force (which does not exist) pushing your body into the car $\endgroup$ – slebetman Jan 25 at 7:02
  • $\begingroup$ @slebetman That's an answer, not a comment. $\endgroup$ – Bill N Jan 25 at 23:18
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You do not feel the centrifugal force. What you feel is the centripetal force (which is the contract/friction force that your seat in your car applies to you) pushing you inward.

Try the following Gedankenexperiment: Imagine your car was not turning, but only being accelerated sideways in a straight line. In which direction would the car have to accelerate, to give you the same feeling you have when turning. In which direction is the force on your car going? You will see, that it's the inwards force that you feel when turning, preventing you from following a straight line.

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but I can't understand that if it is pseudo force then why we feel something pushing us outwards during a tight turn in vehicle.

What you are feeling is is a result of your inertia, or resistance to a change in the direction or magnitude of your velocity per Newton's first law. In this case, your body's resistance to a change in direction from a straight line to a curved path.

If you were driving at constant speed in a straight line and suddenly accelerated the car, you would feel pushed backward. If you suddenly applied the brakes you would feel pushed forward. In each of these cases the "force" you feel is not the result of something physical acting on your body. Instead it's the result of your being in an accelerating (non-inertial) reference frame.

Also, I am very confused that when we will apply centrifugal force, since centrifugal will cancel centripetal force so how will the object move in circle in absence of radial acceleration? (My understanding)

The centrifugal force only cancels the centripetal force in the rotating (non inertial) reference frame. It is only needed to apply Newton's second law to explain why you are not accelerating radially outward in your reference frame. For example, if you are making a hard turn the centrifugal force acts to push you outwards towards, say, the car door. The friction of your seat, or perhaps the car door itself, acts as the centripetal force stopping your outward motion.

In the inertial (non-accelerating) reference frame of the road, only the centripetal force exists and is responsible for your radial acceleration towards the center of your circular motion.

Hope this helps.

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  • $\begingroup$ This is the correct answer. Centrifugal force is not imaginary; as this answer points out, it is absolutely necessary to be a part of the net force, to ensure that the Second Law (also First Law) holds in the accelerating reference frame. $\endgroup$ – DrSheldon Jan 25 at 16:34
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It is not you who is moving outwards and squeezing into the car door. It is the car door which is moving inwards into you.

Your inertia makes your body tend to keep moving straight. Just like when standing in a bus that brakes - you feel pushed forwards, but in fact it is the bus that is being pulled backwards underneath your feet.

When turning, the car door won't allow that your body continues straight. That would break the door. So it pushes you inwards along with it. That is then the centripetal force - it is inwards and there is no other force involved here.

All in all: The "centrifugal force" is merely an illusion. There is no such force. But the centrifugal effect, if we choose to call it that, is very real.

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It is also called fiticious force, or d'Alembert force, or inertial force. I prefer the term inertial force, because we do feel it, not an imagination.

We apply centrifugal force only when we are in a rotational frame, for example we stand on earth, there is a centrifugal force due to the spinning of the earth. The centrifugal force cancles the centripetal force, and makes us on earth without a relative rotation w.r.t earth.

There are other inertial forces generated from derivating a rotational motion on an inertial frame besides centrifugal force, including Coriolis force which making typhoon to turn in a certain direction, $-m \vec{\omega} \times \vec{v}$, and for accelerating rotation frame $- m \frac{d\vec{\omega}}{dt} \times \vec{r}$.

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  • $\begingroup$ Ok so clearly, which reason is apt for explaining our feeling of being pushed outwards, during a tight turn: 1) inertia of path of motion or 2) centrifugal force ? $\endgroup$ – Kshitij Kumar Jan 24 at 18:15
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    $\begingroup$ Centrifugal force is a result of your inertia making you tend to keep moving. away in a straight line centripetal is what keeps you from doing so. $\endgroup$ – Adrian Howard Jan 24 at 18:38
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The key thing you need to understand is that the centrifugal force depends on the reference frame. In some reference frames it exists, in others it doesn't.

Let's take a simple example of a planet orbiting a star at a fixed distance. Before we can analyze their motion, we need to choose a reference frame.

We can choose an inertial reference frame, where there is no centrifugal force. In this frame, the planet moves in a circle. There is one force on the planet - the gravity of the star, which acts as a centripetal force keeping the planet moving in a circle.

Or we can choose a rotating frame, which is centered on the star and rotates with a period equal to the orbital period. In this frame, the planet does not move at all. Its position is completely fixed. There are two forces acting on it - gravity towards the star, and centrifugal force away from the axis of rotation of the frame (which, by construction, means away from the star). The two forces cancel out, so the net acceleration of the planet is 0 (consistent with the observation that it doesn't move at all).

When analyzing more complex systems, we must remember that the centrifugal force applies differently to different objects (the acceleration on each is directed away from the axis of the frame, with magnitude proportional to the distance from the axis); and that there is an additional force, the Coriolis force, which acts on objects which are moving in this frame. (It doesn't come into play in the previous example, because nothing moves.)

In general, whenever you have a system where rotation is involved, you have a choice how to analyze it - either from an inertial frame, or from a rotating frame which matches the system's behavior. Each will lead to correct results, possibly in a different way. But you must be careful not to confuse the two, and apply in one frame logic that belongs to the other.

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