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Consider a situation where a block is kept on a wedge which is further kept on a surface which rotates with $\omega$ the FBD for the same

enter image description here

My question is why dont we consider centripetal force in fbd? Is it because we are drawing it from a frame such that it cancels?


Edit :My simple definition of fbd tells me that it is a diagram representing all the forces acting on the body when viewed from a particular frame which ensures that centripetal force must be acting only in a certain frame

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  • $\begingroup$ From what frame are you analysing the problem? $\endgroup$ Dec 28 '20 at 8:16
  • $\begingroup$ @OVERWOOTCH The person has shown centrifugal force . Isn't it obvious that the frame is a non inertial one. $\endgroup$ Dec 28 '20 at 8:33
  • $\begingroup$ Yes, but it is not obvious which non-inertial frame. I see 2. $\endgroup$ Dec 28 '20 at 8:36
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    $\begingroup$ Note that your accepted answer doesn't really answer your question... $\endgroup$ Dec 28 '20 at 10:09
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    $\begingroup$ Everyone in this thread seems to know what FBD stands for. I count myself as pretty good at physics but I've never heard of the term. So I looked it up and - for the benefit of anyone else in the same position - it's a Free Body Diagram. Incidentally, surely there's a rule which states that a good StackExchange question should explain any abbreviations used, but I can't find such a thing so maybe not. $\endgroup$ Dec 28 '20 at 21:35
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From an inertial frame

You are considering the centripetal force. In fact you have already included it if you are using an inertial frame.

The centripetal force is not a new force. It is just a name we give to whichever force that pulls centripetally (towards the centre in circular motion).

In your case there is a component from the normal force which pulls centripetally (horizontally leftwards). So that is called the centripetal force.

From the non-inertial frame

This above explanation is from an inertial frame, as if standing on the ground and watching the scenario. If you want to look at this from a non-inertial frame, by imagining that you are sitting on the block that is in rotation, which might be the case judging from your sketch, then from that frame the block doesn't seem to rotate. Rather it looks like the surroundings are "rotating".

Thus from that frame there seems to be no (resultant) centripetal force acting on the block. This means that the horizontal component of the normal force must be balanced out by something. That "something" is what we invent with the name centrifugal force, pointing opposite in the outwards direction.

This centrifugal force is a so-called pseudo-force in that it doesn't really "exist" - but we invent it mathematically in order to make Newton's laws hold true even in non-inertial frames.

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  • $\begingroup$ First you say "In your case there is a component from the normal force which pulls centripetally", i.e. it is a real force. I think it is misleading to say "Thus from that frame there is no centripetal force acting on the block.", since the real force could not have vanished. I think it would be more accurate to say that in the non-inertial frame the block is stationary, thus the centripetal force must be balanced by something. $\endgroup$
    – LLlAMnYP
    Dec 28 '20 at 18:27
  • $\begingroup$ @LLlAMnYP My words are that from that frame there doesn't seem to be rotation and thus no centripetal force is observed. But I agree, the next sentence you mention could be interpreted a bit off, so I've made an edit. Thanks for pointing this out. $\endgroup$
    – Steeven
    Dec 28 '20 at 18:35
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The reason we don't include the "centripetal force" in the FBD is the same reason we don't include the "vertical force" or the "horizontal force" in the FBD. Centripetal is just a direction, just like vertical and horizontal are directions. Just like how forces can be vertical or horizontal, forces can also be centripetal or tangential.

For example, including "centripetal force" on a FBD would just be like including the gravitational force as well as a second "vertical force" on the FBD for an object in free fall. In your case, there is a component of the force of the wedge on the block. This force points in the centripetal direction, so it is a centripetal force. But you wouldn't put an explicit "centripetal force" on the diagram; you already did that.

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  • $\begingroup$ Ok this gives me another doubt that centrifugal and centripetal are synonymous except for direction but in the frame of wedge both must be experiencing centripetal as well as centrifugal force which means even centrifugal force shouldn't be included $\endgroup$
    – Anusha
    Dec 28 '20 at 13:40
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    $\begingroup$ @Anusha In a rotating frame you would include the centrifugal force on the FBD. It is an actual "force" in that case. "Centrifugal" in this case is not just a direction indicator (although I can see where the confusion lies, since technically centrifugal is a direction). $\endgroup$ Dec 28 '20 at 14:32
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My question is why dont we consider centripetal force in fbd ? Is it because we are drawing it from a frame such that it cancels?

Centripetal force and centrifugal force never act together. You are working in non-inertial frame and have shown centrifugal force , hence no need to show centripetal force.


I am attaching a picture from my notes to clarify what i meant so that my answer is interpreted correctly. The situation is quite similar to your question.

Consider a case of banking when viewed from 2 different frames :

Inertial frame

In ground frame , you don't show any centrifugal force.

Inside Car

From inside car, which is a non inertial frame ,$F_{centrifugal}$ is balanced by $Nsin\theta$. No doubt $Nsin\theta$ will act in both frame , and is equal to $mv^2/r$ regardless of the frame but since car is at rest in non inertial frame , I wouldn't call it a centripetal force.


Edit 2 :

Why would i call $Nsin\theta$ a centripetal force in the car's frame

According to Wikipedia a centripetal force is defined as : a force that makes a body follow a curved path. Since the body is at rest in it's own frame , $Nsin\theta$ is is not a cause of the centripetal force in the rotating frame.

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    $\begingroup$ Isnt centrifugal force a pseudo force? Which means it should be drawn in inertial frame $\endgroup$
    – Anusha
    Dec 28 '20 at 7:09
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    $\begingroup$ @Anusha Pseudo Force acts in non inertial frame of reference . $\endgroup$
    – Bhavay
    Dec 28 '20 at 7:13
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    $\begingroup$ This answer is misleading. Centripetal force doesnt “act” in any frame of reference. Centripetal “force” is merely a component of the net force that points towards the centre of curvature and is perpendicular to the velocity at all times. It is akin to horizontal force or vertical force. Horizontal and vertical forces dont “act”; instead, forces like gravitation, electromagnetic, normal contact, friction etc... constitute a net force that HAS horizontal snd vertical components. In the same way, the net forces of objects in circular morion have centripetal components. $\endgroup$ Dec 28 '20 at 8:21
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    $\begingroup$ This is completely incorrect. Non-inertial frames don't make centripetal forces disappear. $\endgroup$ Dec 28 '20 at 14:35
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    $\begingroup$ Your first statement is still incorrect. $\endgroup$ Dec 28 '20 at 15:33
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why dont we consider centripetal force in fbd ?

Indeed, we should include pseudo forces too, consider this :

enter image description here

Due to different position of wedge and block COM from rotational axis and they difference in mass- there will arise subtle tidal forces (differences in centrifugal forces of that within block and wedge). So in the end normal force upon block will be :

$$ N = mg \cdot \cos \alpha + m\,\omega^2r \cdot \sin\alpha - M\omega^2R \cdot \sin\alpha$$

Where $m$ block mass, $M$ - wedge mass, $r$ block distance from rotational axis, $R$ - wedge distance from rotational axis, $\omega$ - angular speed.

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The descriptions of circular motion often make it sound like centripetal and/or centrifugal force result from circular motion. But it's the opposite: circular motion results from centripetal force. There is nothing specifically exerting a centripetal force on the object. Centripetal force is an "output" force, not an "input" force. Gravity and the normal force are the "input" force; they are distinct forces from distinct physical sources. When we add those two forces together, we get the net force. Since this force is toward the center of the circle, it is a centripetal force. "Centripetal force" is just what we're calling the sum of all the input forces. It's not a force we start with when we're drawing the FBD, it's what we use the FBD to find.

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We do not consider the centripetal force to only be acting on the block, as it is also acting on the wedge. You have to consider the entire wedge-block system while calculating the centripetal force, so the centripetal force would act on the wedge-block system as a whole, not only on the block.

Edit:

Even if you do consider the centripetal force, then you have to consider a horizontal component of reaction from the wedge which correctly cancels out the centripetal force, so it won't make any difference. I hope this helps!

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