Rolling Disk: dynamics versus energy analysis

[Taulant Sholla]

Homework Statement

If the cylinder starts from rest and rolls without slipping, what is the speed of its
center of mass after it has rolled through a distance d?

Relevant Equations

torque = force x moment arm
work = change in kinetic energy

I got the correct answer (according to the textbook) using dynamics (steps 1-8 in blue as shown in the attached image).
I get a different answer using work-kinetic energy theorem (steps 1-7 in green as shown in the attached image).

Where am I going wrong?

 

[Orodruin]

First of all, do not provide your work as an image. It becomes impossible to quote particular sections.

As for your issues, there are several. Most are related to your step 4 where you make several faulty assumptions. Please type out your steps and provide your reasoning for each.

Edit: Note: Correct application of the work-energy theorem will give the correct result.

 

[Taulant Sholla]

First, don't worry about quoting sections; simply reference the numbering shown in the image. This is a much more efficient approach v. cumbersome typing/equation editing. You should accommodate alternative presentation approaches; don't require others to adhere to your particular style. Be flexible.

I assume you are referring to step 4 for the energy analysis approach (go ahead and just state this). If this is correct, then for energy analysis step 4.

Left side: force x distance = mad, where a is the acceleration expression found, correctly from the dynamics approach. This is clearly shown in my work.

Right side of step 4: there are 2 kinetic energies: rotational and translational. (1/2)mv^2 is translational and (1/2)*I*w^2 is rotational. Omega (w) is shown as (2Vcm/R) as clearly shown. The rotational speed of a point on the rim is twice that of Vcm, so w=2Vcm/R (again, this is already clearly shown).

I is the rotational inertia of a disk: I = (1/2)MR^2

(like I said, typing these equations out is super inefficient; images are better).

The rest is algebra.

Clearly I'm making an error somewhere. Please focus on asking me questions relating to the work I've shown and in the manner I've shown it. I'm happy to provide more detail.

I welcome and appreciate your help in this regard, but be open and less dogmatic in terms of how others present their work (e.g. images versus cumbersome equation typing). Refer to the specific sections and numbering I've clearly laid out.

 

[Orodruin]

First, don't worry about quoting sections; simply reference the numbering shown in the image.

That is not how things are done. You are seriously going to question the modus operandi? Well then, forget about my help.

This is a much more efficient approach v.

For you perhaps (doubtful though). Not for the people you are asking for help. Reading typed out text - preferably with a typed out reasoning as well - is significantly easier for a helper. As is being able to quote and manipulate particular sections. You are basically saying that this is what is more convenient for you, who cares about the people you are asking yo help you for free?

force x distance = mad

Wrong. That force is not the only force acting on the cylinder. Furthermore, the distance is wrong.

When you insert the acceleration from thd previous analysis you are effectively writing $F=4F/3$ or, equivalently $4=3$, which is absurd.

Omega (w) is shown as (2Vcm/R) as clearly shown.

Wrong again. Think about this one. Why would that be the case? You have not provided any valid reason to assume so.

like I said, typing these equations out is super inefficient; images are better

Nonsense. It may be more convenient for you. You are again saying you don’t care about the people you ask for help.

but be open and less dogmatic in terms of how others present their work (e.g. images versus cumbersome equation typing). Refer to the specific sections and numbering I've clearly laid out.

You are the one violating forum guidelines just because it is more convenient for you - caring nothing for helpers. This indicates laziness and entitlement on your part. This will be my last reply here.

 

[haruspex]

For you perhaps… Not for the people you are asking for help.

And there are multiple readers per writer.

 

[Taulant Sholla]

That is not how things are done. You are seriously going to question the modus operandi? Well then, forget anout my help.

You don't seem well suited for modern online discourse. "This is not how things are gone" is the quintessence of closed mindedness. Providing a clear image showing side-by-side sections, with each step numbered, is clear and easy to follow. Try being more flexible.

For you perhaps (doubtful though). Not for the people you are asking for help.

You speak for everyone? Other PF responders absolutely do not don't hold your views. Don't try to speak for anyone other than yourself. Again, how much easier can my work be to follow: I've laid out everything in clearly labelled, side-by-side sections with numbered steps and supporting visuals.

Reading typed out text - preferably with a typed out reasoning as well - is significantly easier for a helper. As is being able to quote and manipulate particular sections.

You could have just stated: "Look at #4 in your ENERGY section and please say more about how you developed this." How much easier could this be? Also, speak for yourself, don't try to speak for other "helpers." They can speak for themselves.

You are basically saying that this is what is more convenient for you, who cares about the people you are asking yo help you for free?

How does PF not encourage volunteers to not engage in a pleasant and respectful manner? I mean, look at the vitriol you're expressing here. How is this allowed?

I volunteer as a homework helper for other subjects. I regard my students as my customers despite the fact I'm the one helping them. I always strive to provide courteous and pleasant customer service.

I accommodate an array of diverse styles, as long as they are clear and coherent. You should try to do the same. Tersely scolding people asking for help off-putting.

Wrong. That force is not the only force acting on the cylinder. Furthermore, the distance is wrong.

Thanks; this is super helpful, pleasant and engaging. Great bedside manner; great example of the Socratic Method.

When you insert the acceleration from thd previous analysis you are effectively writing $F=4F/3$ or, equivalently $4=3$, which is absurd.

Does referring to my work as absurd fall with the etiquette guidelines provided by PF? Also, consider spell-checking your writing.

Wrong again. Think about this one. Why would that be the case? You have not provided any valid reason to assume so.


Nonsense. It may be more convenient for you. You are again saying you don’t care about the people you ask for help.


You are the one violating forum guidelines just because it is more convenient for you - caring nothing for helpers. This indicates laziness and entitlement on your part. This will be my last reply here.

"wrong again"
"absurd"
"nonsense"
"laziness"
Are these terms consistent with "forum guidelines" you refer to?

Lastly, please spell- and grammar-check your writing.
smh

 

[erobz]

If we are going to reply to the handwritten ( many times practically illegible work) we are going to have to re-write it in Latex anyhow - Personally, I ask them to use Latex too. It’s easy to learn and crystal clear formatting for everyone reading this forum. Give it a try, please... Latex Guide

As @Orodruin says below explain your thinking in words along with it. Pretend you are writing a technical paper. There is another reason to do this that you may not have considered...in gathering one's thoughts to explain them to someone else, you'll "inadvertently" slow down and you might find your error, or/at least notice something inconsistent(other than the answers).

 

[Orodruin]

Lastly, please spell- and grammar-check your writing.
smh

Says the one presenting their writing as quotes of the other.

Did you stop for one second to consider yourself at fault? Speaking of bedside manners, how do you think a doctor would react if the patient insisted that they be examined lying on their belly when the doctor asks them to sit up and on top has the audacity to claim that examination belly down is perfectly fine? This is a patient attitude problem, not a doctor attitude problem.

And no, your work is not as easy to follow as you may think. Particularly it is missing any form of supporting thought process spelling out what you are actually doing. Just listing equations does not convey the thought process properly. This is particularly the case when there are errors in the process.

 

[berkeman]

Thread is closed temporarily for Moderation...

 

[berkeman]

Thread will remain closed.

@Taulant Sholla -- If you wish to re-start an improved version, please do so using LaTeX and try to incorporate the fixes that have been suggested in this thread.