Radius of Circular Disc for Mech. Engr Problem

  • Thread starter Thread starter Robust
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around determining the radius of a circular disc based on a specified area of 16 units. Participants explore the implications of whether the area refers to the cross-sectional area or the total surface area, and how this affects the calculations involved.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests using the formula for the area of a circle, A = πr², to derive the radius from the given area of 16 units.
  • Another participant proposes a rearrangement of the formula, stating that the radius can be calculated as sqrt(area/π), leading to a radius of approximately 2.2567 units.
  • Concerns are raised about whether the area specified is the cross-sectional area or the total surface area of the disc, with implications for the necessary parameters to determine the radius.
  • Some participants express uncertainty about the relevance of π in the calculations, suggesting that the radius remains consistent regardless of the π value used.
  • There is a discussion about the need for thickness if the total surface area is considered, as it involves two circular surfaces and the circumference strip.
  • One participant emphasizes the importance of returning to basic formulas and critical thinking when solving mathematical problems.

Areas of Agreement / Disagreement

Participants express differing views on whether the area in question is the cross-sectional area or the total surface area, leading to multiple competing interpretations of the problem. The discussion remains unresolved regarding the implications of these interpretations on the calculations.

Contextual Notes

Some participants note that the problem as originally stated indicated the total surface area, which introduces additional complexity regarding the thickness of the disc. There is also mention of potential confusion surrounding the use of π in the calculations.

Robust
Messages
18
Reaction score
0
A mechanical engineer requires the turning of a circular disc giving an area of 16 units. What radius does he give the machinist?
 
Engineering news on Phys.org
What is an equation for area that involves the radius?

You have the area...You have a constant [tex]\pi[/tex]...
 
FredGarvin said:
What is an equation for area that involves the radius?

You have the area...You have a constant [tex]\pi[/tex]...
The equation I would give is: sqrt area/sqrt pi = radius; thus, if an area 16 then 4/1.77245...= 2.2567...radius. r^2*pi = 16 area

I took a bit of abuse by contempories for this formula - wanted to hear what Y'all might think of it.
 
Looks good to me Robust.

Check that the given area is the cross sectional area, and not the total surface area of the disc. If this is so, you're spot on.

Don't be so quick to take abuse from contemporaries! Too many times I've lost face and backed down, only to find that I was right all along...
 
brewnog said:
Looks good to me Robust.

Check that the given area is the cross sectional area, and not the total surface area of the disc. If this is so, you're spot on.

Don't be so quick to take abuse from contemporaries! Too many times I've lost face and backed down, only to find that I was right all along...
Thanks for the confirmation, but I'm not out of the woods yet on this, for the problem as originally given (project engineer) did state the total surface area, the tolerance being incidental. The PE is one of those who likes to throw these kinds of questions at us, just to keep us on our toes I suspect.

But the implications of this one does present a serious conflict as regards the pi value, showing it to be irrelevant. the radius is given consistently regardless of the pi pi value employed (recognized pi values). Here is the given formula: sqrt area/sqrt pi = radius; r^2*pi = 16 area!
 
Robust said:
But the implications of this one does present a serious conflict as regards the pi value, showing it to be irrelevant. the radius is given consistently regardless of the pi pi value employed (recognized pi values). Here is the given formula: sqrt area/sqrt pi = radius; r^2*pi = 16 area!

I am not quite following you on this. All your PE is doing is restating the equation for the area of a circle in different ways. Nothing is different. Pi is Pi is Pi is Pi...
 
If the PE is giving you the total surface area of the disc, this means you'll need to also know its thickness, - the total surface area comprising of two circular surfaces, and a 'strip' to go around the periphery.
 
brewnog said:
If the PE is giving you the total surface area of the disc, this means you'll need to also know its thickness, - the total surface area comprising of two circular surfaces, and a 'strip' to go around the periphery.
It's a hypothetical question. the thickness and other parameters are immaterial. Only the radius to the circular plane is required.
 
Robust.

Were you given the cross sectional area of the disc, in which case you're just rearranging the formula for the area of a circle, or were you given the total surface area of the disc.

If it's the latter, then the thickness is imperative, because you are considering two equal circular surfaces, and the 'strip' around the circumference. If the former is the case, your problem is pretty trivial, and Fred gave you the answer (in fact, you worked it out yourself!).
 
  • #10
Never before has so much discussion devolved from the simple formula, A = pi*r^2...;)
 
  • #11
Robust said:
the problem as originally given did state the total surface area

I'm not nitpicking here am I?
 
  • #12
brewnog said:
I'm not nitpicking here am I?
Knitpicking is fine with me - probably the more the better!
 
  • #13
pack_rat2 said:
Never before has so much discussion devolved from the simple formula, A = pi*r^2...;)
Not so simple considering the absurdity of the area to a closed continuum described by other than a whole number or ending decimal.
 
  • #14
No mentor/ just a comon sense approach

I guess with questions concerning math problems, I go back to the basic formula. A=pi*r^2. Then simply factor it, to put the term you are looking for on the correct side of the = sign. r=sqrt(A/pi). A simple and basic approach to solving problems is always the best way to solve the problem. Any time a person tries to get out of their comfort zone, problems usually arise (wrong solution.) The best way to expand your comfort zone is to study study study. And, read forums like this to keep your mind open to the possibility that there may be more than approach to solving a problem. " Critical thinking starts with you."
 

Similar threads

Did working as a MechE help you learn about tools in a machine shop?
  • · Replies 10 ·
Replies
10
Views
3K
DC Motor for 6kg Aluminium Disc at 1600rpm
  • · Replies 5 ·
Replies
5
Views
1K
Can you help me calculate the required torque and power of this motor?
  • · Replies 8 ·
Replies
8
Views
3K
High School Accuracy of a smith's crafted metal disc
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad KE of rotating disc
  • · Replies 87 ·
3
Replies
87
Views
7K
Where Can I Find an Affordable One-Way Rotation Mechanism?
  • · Replies 7 ·
Replies
7
Views
7K
Shear Stress between Two Rotating Discs
  • · Replies 5 ·
Replies
5
Views
6K
Placing a pole with maximal radius subject to constraints
  • · Replies 3 ·
Replies
3
Views
1K
Mechanical problem -- Joining 2 metal strips with some sort of hinge
  • · Replies 5 ·
Replies
5
Views
2K
High School Relative rate of clock ticks on the radius of a rotating disc
  • · Replies 46 ·
2
Replies
46
Views
4K