Acceleration in uniform circular motion is uniform or non-uniform?

[Darshit Sharma]

Homework Statement

Centripetal acceleration in uniform circular motion is uniform or non-uniform?
Which kind of force acts on the hand and its direction?

Relevant Equations

No equations

I had an exam ques which was as follows:

The first part is clear to me.....it is uniform (or constant) speed.

I am in doubt on the account of the second part as the answer key says this:

So the overall question concerning the second part is as follows:

We know that the direction of centripetal acceleration is ever-changing and since acceleration is a vector quantity we must conclude that the acceleration is non-uniform but the answer keys says the contrary.

Please don't give answers which are vague in this context like "It is uniform in magnitude but not non-uniform in direction." I truly understand it may be the case which is true but what I am seeing here is the answer to this question which has just Yes No option.



Now for the third part,
I believe that centrifugal force should not be the answer because centrifugal force acts on the body undergoing the circular motion, hence it should be the stone on which both centripetal and centrifugal forces are acting.

So does anyone have any clue about which force could be acting on the hand and its direction?

Another source (my textbook) says:
"Reaction of tension away from the centre of the circular path"

But isn't this same ass the centrifugal force? Doesn't all this contradict "centrifugal force acts on the body undergoing the circular motion"? And if not, then which force provides for the centrifugal force?

 

[Hill]

what I am seeing here is the answer to this question which has just Yes No option.

My answer is, No.

 

[Darshit Sharma]

My answer is, No.

Okay sir
And the force on hand?

 

[Hill]

Okay sir
And the force on hand?

Centrifugal.

 

[kuruman]

Please don't give answers which are vague in this context like "It is uniform in magnitude but not non-uniform in direction." I truly understand it may be the case which is true but what I am seeing here is the answer to this question which has just Yes No option.

What is your understanding of "uniform acceleration?" How would you know it if you saw it? If you don't know, look it up. There are plenty of examples on the internet which will enable you to answer your own question.

By the way, if you found this problem here, the so called answers to the question are shown below. The answer to (ii) is wrong and maliciously misleading.

I believe that centrifugal force should not be the answer because centrifugal force acts on the body undergoing the circular motion, hence it should be the stone on which both centripetal and centrifugal forces are acting.

That's nonsense. The centripetal and centrifugal forces have equal magnitudes and opposite directions. If both acted on the stone, the net force on it would be zero and the stone would move in a straight line.

 

[berkeman]

Please don't give answers which are vague in this context like "It is uniform in magnitude but not non-uniform in direction."

"Vague"? I think you meant to write "Please don't give answers which are correct in this context"...

 

[Darshit Sharma]

"Vague"? I think you meant to write "Please don't give answers which are correct in this context"...

Sorry for my english skills.

 

[berkeman]

No need to say sorry. I'm just saying that the answer key looks correct to me.

 

[Darshit Sharma]

That's nonsense. The centripetal and centrifugal forces have equal magnitudes and opposite directions. If both acted on the stone, the net force on it would be zero and the stone would move in a straight line.

But if we are in a non-inertial reference frame, then no net force acts on the body right, it seems as if it were in rest, isn't it?

Moreover my textbook says that centrifugal force act on the same body.....and as it has same magnitude diff direction it counterbalances the centripetal force....

 

[Darshit Sharma]

No need to say sorry. I'm just saying that the answer key looks correct to me.

Sorry to be in such a hurry and for such hopelessness. I just chilled on 4 days of holiday and I'm having the physics exam right after 2h. So much chaos......

But sir @kuruman says something different.....
And I too feel that he is correct because I also don't see the acceleration as uniform beacuse the direction is changing

 

[berkeman]

And I too feel that he is correct because I also don't see the acceleration as uniform beacuse the direction is changing

Acceleration would usually be a vector, but I suppose it could just be the magnitude of the accleration. It depends on how the question is asked.

 

[Darshit Sharma]

Acceleration would usually be a vector, but I suppose it could just be the magnitude of the accleration. It depends on how the question is asked.

The verbatim question is presented before you sir, what do you think would be the most apt answer....Yes or No? Yes?
and @kuruman yours, sir?

 

[kuruman]

Part (ii) is questionable. Uniform acceleration implies motion in a straight line and equal changes in velocity in equal times just like uniform velocity is motion in a straight line and implies equal changes in position in equal times.

What we have here is uniform circular motion which implies motion in a circle of constant radius at constant speed.

 

[Darshit Sharma]

Centrifugal.

I've attached some pictures in #9 sir..please have a look

 

[kuruman]

I've attached some pictures sir..please have a look

Where are they attached?

 

[Darshit Sharma]

Part (ii) is questionable. Uniform acceleration implies motion in a straight line and equal changes in velocity in equal times just like uniform velocity is motion in a straight line and implies equal changes in position in equal times.

What we have here is uniform circular motion which implies motion in a circle of constant radius at constant speed.

Yes but as Velocity is non-uniform (my textbook says this) on the only basis of its direction......we can confidently say that acceleration is non-uniform on the very basis of its direction
(which my textbook doesn't say, it neither say uniform nor non-uniform but the question was there in the test 10 years ago)

 

[Darshit Sharma]

Where are they attached?

in #9

 

[Darshit Sharma]

I am so much thankful to all of you for answering to such ill-formed messages and replies @kuruman @berkeman @Hill Let us reach a single final answer to (ii) and (iii) with plausible explanation.

 

[kuruman]

I am so much thankful to all of you for answering to such ill-formed messages and replies @kuruman @berkeman @Hill Let us reach a single final answer to (ii) and (iii) with plausible explanation.

You have the evidence before you. What is your conclusion?

 

[kuruman]

in #9

Yes, I see them now but I cannot read sideways.

 

[Darshit Sharma]

You have the evidence before you. What is your conclusion?

ii) Non-uniform

I am not sure about (iii) yet as sir you are saying that centrifugal force doen't acts on the stone, @Hill is saying that it does so and the textbook also says.....

Perplexed..

 

[haruspex]

we must conclude that the acceleration is non-uniform

Agreed.

centrifugal force should not be the answer because centrifugal force acts on the body undergoing the circular motion, hence it should be the stone on which both centripetal and centrifugal forces are acting.

The force thats on the hand is clearly the tension in the rope.
Not sure that you meant both centripetal and centrifugal forces act on the stone at the same time. More likely, I hope, you meant that one or the other acts, depending on the reference frame.

But in my view that is not right either.
Centripetal force is a component of the net of all the forces that act on the body. Specifically, it is the component normal to the velocity. It is not another force acting on the body.
Centrifugal force is a force that acts on the body, so contributes to the net force. It is a force we have to invent when using a noninertial frame.
If we choose a frame fixed in relation to the body then in that frame there is no acceleration. The centrifugal force is necessarily equal and opposite to the net of all other forces.
What is under appreciated is that we could choose some other noninertial frame. In this case we can have a centrifugal force contribution and a nonzero centripetal resultant.

 

[Darshit Sharma]

Yes, I see them now but I cannot read sideways.

You mean you can't read in the orientation pictures are sent or you want me to send the pictures of the whole page?

 

[kuruman]

You mean you can't read in the orientation pictures are sent or you want me to send the pictures of the whole page?

That's OK. Please don't bother reposting them.

 

[Darshit Sharma]

What is under appreciated is that we could choose some other noninertial frame. In this case we can have a centrifugal force contribution and a nonzero centripetal resultant.

Haha, I'' surely study it after my exams....you guys are making me love physics...

The force thats on the hand is clearly the tension in the rope.

Tension is acting as the "component normal to the velocity," i.e. centripetal force and we know that centripetal force acts on the body undergoing the motion....so how can tension act on hand.....you mean to say reaction of tension?

 

[Darshit Sharma]

That's OK.




So sir....@haruspex and my textbook are of the view that centrifugal force acts on the body.....so sir what do you say now which force acts on the hand, it it centrifugal force? or is it the reaction force of the tension or something just completely out of the box?

@berkeman Sir do you still stand still with the answer (iii) in the answer key?

 

[Darshit Sharma]

Haha, I'' surely study it after my exams....you guys are making me love physics...


Tension is acting as the "component normal to the velocity," i.e. centripetal force and we know that centripetal force acts on the body undergoing the motion....so how can tension act on hand.....you mean to say reaction of tension?

Centrifugal force is a force that acts on the body, so contributes to the net force. It is a force we have to invent when using a noninertial frame.

What I recalled just now sir beacuse of you is that there is only one case where we assume centrifugal force, i.e. in a non-inertial frame....so this removes any further possibility of two cases for (iii).....let's see what is the final single correct answer for iii

 

[Darshit Sharma]

I would really be grateful if we could arrive the final answer for iii within 25-30 minutes. I know it might be late night somewhere in the world....but this act of generosity would surely be venerated.

 

[haruspex]

Haha, I'' surely study it after my exams....you guys are making me love physics...


Tension is acting as the "component normal to the velocity," i.e. centripetal force and we know that centripetal force acts on the body undergoing the motion....so how can tension act on hand.....you mean to say reaction of tension?

Tension in a rope acts on whatever is attached at each end. If the rope is massless or not accelerating, and not subject to other forces along its length, then the two exerted forces are equal and opposite.

 

[haruspex]

I

I would really be grateful if we could arrive the final answer for iii within 25-30 minutes. I know it might be late night somewhere in the world....but this act of generosity would surely be venerated.

I gave you my final answer.
If you insist on choosing between centripetal and centrifugal (or both), you have to define your frame first.

 

[Darshit Sharma]

Tension in a rope acts on whatever is attached at each end. If the rope is massless or not accelerating, and not subject to other forces along its length, then the two exerted forces are equal and opposite.

Is there anything known as "Reaction force of tension" If yes then it acts on what in this case?

 

[Darshit Sharma]

I gave you my final answer.
If you insist on choosing between centripetal and centrifugal (or both), you have to define your frame first.

No sir...I ain't insisting on anything....
Let me confirm my understanding of your final answer for the force on the hand"

Inertial reference frame: "Tension"
Non-inertial reference frame: "Tension"

If I am not wrong this is what you mean to convey sir, right? And where is the reaction of tension force?

 

[haruspex]

Is there anything known as "Reaction force of tension" If yes then it acts on what in this case?

Tension (likewise compression) is not exactly a force. It is more like pairs of equal and opposite forces acting all along the rope. Only at the two ends, where there is no "pair", does it manifest as a force.
The reaction to that is the force exerted by the object attached to it. But you are not asked what force the hand exerts; you are asked what force is exerted on the hand.

 

[Darshit Sharma]

Tension (likewise compression) is not exactly a force. It is more like pairs of equal and opposite forces acting all along the rope. Only at the two ends, where there is no "pair", does it manifest as a force.
The reaction to that is the force exerted by the object attached to it. But you are not asked what force the hand exerts; you are asked what force is exerted on the hand.

Ohk sir.........So the hand's exerted force and the rotating stone's weight are the reaction to tension.

So, here we are finally concluding the answer as "Tension."


I had one last doubt, It appears from the diagram I drew that "Tension" is not only the centripetal force here but also the centrifugal force, is it right? and the this "tension" that is in my diagram should exist in inertial reference frame also......so centrifugal force in inertial refernce frame, it doesn't seems to make any sense?

 

[Darshit Sharma]

@haruspex Sir I noticed you deleted your answer "Yes", anything serious?

 

[Hill]

I've attached some pictures in #9 sir..please have a look

I've changed my answer on (iii). The force that is exerted on the hand is not what is defined as centrifugal force.

 

[Darshit Sharma]

I've changed my answer on (iii). The force that is exerted on the hand is not what is defined as centrifugal force.

Ok sir, so you are also with "Tension"?

 

[Hill]

Ok sir, so you are also with "Tension"?

The rope exerts this force on the hand.

 

[Darshit Sharma]

The rope exerts this force on the hand.

Yes so it is tension only right? Tension is the force the rope exerts on its both ends? Right?

 

[haruspex]

Moreover my textbook says that centrifugal force act on the same body.....and as it has same magnitude diff direction it counterbalances the centripetal force....

I don’t see where it says they counterbalance. What it fails to make clear is that (with the usual choice of noninertial frame) you have one or the other, never both.
I have no idea what they mean about action and reaction not acting on the same body.

What they should have stressed is that when centrifugal force applies it does so exactly like any other applied force, whereas centripetal force is not another applied force: it is just what we call a particular component of the net of all the acting forces. It is very important that you grasp that.

Inertial reference frame: "Tension"

Yes.

Non-inertial reference frame: "Tension"

Yes.

 

[Darshit Sharma]

I don’t see where it says they counterbalance.

My teacher told me so, sir. He said they both counterbalances and cancel themselves.


What it fails to make clear is that (with the usual choice of noninertial frame) you have one or the other, never both.

Never both, why sir? we do have centripetal and centrifugal force, right?

I have no idea what they mean about action and reaction not acting on the same body.

What sir? My textbook says they are not forces of action and reaction (N3LM) becuase action and reaction act on different bodies while these both foces act on the same body, in our case the stone.
Is this correct explanation sir?

What they should have stressed is that when centrifugal force applies it does so exactly like any other applied force, whereas centripetal force is not another applied force; it is just what we call a particular component of the net of all the acting forces. It is very important that you grasp that.



OK sir

 

[Hill]

Yes so it is tension only right? Tension is the force the rope exerts on its both ends? Right?

Tension in the rope is the origin of this force.
I am talking about the force exerted on the hand by the rope -- not the force exerted on the end of the rope.

 

[Darshit Sharma]

Tension in the rope is the origin of this force.
I am talking about the force exerted on the hand by the rope -- not the force exerted on the end of the rope.


Oh, is there any name to this, sir?

I strongly believe that all this thing is going on with contact forces and the point of contact is the end point, so sir doesn't @haruspex "Tension more apt"?

 

[Hill]

I strongly believe that all this thing is going on with contact forces and the point of contact is the end point, so sir doesn't @haruspex "Tension more apt"?

I think that "the force exerted on the hand by the rope" is perfect name for it.

 

[haruspex]

You have made responding a bit awkward by embedding your responses in your quotes of my posts. It means I cannot use the quote button on them.

"My teacher told me so, sir. He said they both counterbalances and cancel themselves."
Oh dear. Your teacher is incompetent. You have my sympathy.
"Never both, why sir? we do have centripetal and centrifugal force, right?"
As I wrote, in an inertial frame there is no centrifugal force; in the noninertial frame locked to the body, the body is not moving, so there is no centripetal acceleration nor force. In some other noninertial frame there can be both, but it would be a very odd choice of frame.

 

[Orodruin]

That's nonsense. The centripetal and centrifugal forces have equal magnitudes and opposite directions. If both acted on the stone, the net force on it would be zero and the stone would move in a straight line.

Centrifugal force is a force that acts on the body, so contributes to the net force. It is a force we have to invent when using a noninertial frame.

This is the centrifugal vs reactive centrifugal force debate all over again. The first is a non-inertial force in the co-rotating frame, in which the object is indeed at rest, and the latter is the third law pair of the centripetal force.

Ultimately, the answer key here should state “reactive centrifugal” rather than just “centrifugal” to be technically correct (the best form of correct).

 

[haruspex]

This is the centrifugal vs reactive centrifugal force debate all over again.

Is it? I see nothing discussed in the thread till now which would be described as the reactive centrifugal force…

the answer key here should state “reactive centrifugal” rather than just “centrifugal”

… which would be the force the stone exerts on the string, not a force exerted on the hand.

 

[Orodruin]

Is it? I see nothing discussed in the thread till now which would be described as the reactive centrifugal force…

… which would be the force the stone exerts on the string, not a force exerted on the hand.

That’s splitting hairs. Most high school teachers will not go into details here, but consider the string as either part of “ball” or “hand”. It depends on how you divide your situation into systems.

Edit: And even if you consider the string its own system, the force from the string on the hand is the reactive centrifugal force of the string.

 

[haruspex]

It depends on how you divide your situation into systems.

Ok, but that makes the question unanswerable.

 

[Steve4Physics]

Hi @Darshit Sharma. I’d like to add this…

Let's assume that the path of the mass is a circle in the horizontal plane (otherwise a uniform speed is hard to achieve).

.Note that the centre of rotation is a point vertically below the hand (because the string can never be perfectly horizontal). We have to be very careful when we refer to directions as 'radially' inwards or outwards - do we mean with respect to the centre of rotation or with respect to the hand?
_______________

The answer to question (i) is: Uniform speed

Comment: The problem-statement explicitly states that the mass is moving ‘with a uniform speed’. So question (i) seems pointless.
_______________

An acceptable (IMO) answer to question (ii) is:

The magnitude of the acceleration is uniform (constant). But since the direction of the acceleration continually changes, the acceleration (a vector) is non-uniform.

The direction of the mass's acceleration is radially inwards towards the centre of rotation.

Comment: The answer in the answer-key is unsatisfactory at-best, and wrong at-worst.
_______________

An acceptable (IMO) answer to question (iii) is:

The force acting on the hand is the tension at the (inner) end of string. It’s direction is towards the mass.

An alternative acceptable (IMO) answer is that the force acting on the hand is the frictional force of the string on the hand, acting towards the mass.

Comment: The answer in the answer-key is wrong about the force. The hand is effectively stationary in an inertial frame of reference and therefore never experiences a ‘centrifugal force’.

EDIT: Some changes to improve answer.