Calculating Uncertainty: What is the Effect of θ?”

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The discussion focuses on calculating uncertainty in the variable θ, emphasizing the relationship between fractional error and actual uncertainty. It clarifies that while smaller values of θ lead to smaller actual uncertainty, the percentage uncertainty remains constant across different values of θ. The participants debate the validity of various options in a homework problem, ultimately concluding that option A is incorrect. A distinction is made between fractional uncertainty and fractional error, with the consensus that they can be treated similarly in this context. The conversation concludes with an understanding that percentage uncertainty is consistent, while actual uncertainty varies with θ values.
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Homework Statement


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Homework Equations


Absolute uncertainty in θ = δθ/θ

The Attempt at a Solution


I know that smaller θ gives smaller actual uncertainty, thus leaving B and D out. The answer is C. but what about option A?
 
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Your relevant equation is wrong.
If the fractional error in X is r, how large is the actual error in X? How large then is the actual error in theta?
 
haruspex said:
Your relevant equation is wrong.
If the fractional error in X is r, how large is the actual error in X? How large then is the actual error in theta?
The actual error in X would be rX? And rθ?
 
Janiceleong26 said:
The actual error in X would be rX? And rθ?
Yes. So what is the fractional error in theta?
 
haruspex said:
Yes. So what is the fractional error in theta?
r ?
 
Janiceleong26 said:
r ?
Right. Can you now see why A is wrong?
 
haruspex said:
Right. Can you now see why A is wrong?
No ..sorry..
If actual uncertainty in θ is r, then the percentage uncertainty of θ would be r x100 right? Isn't the effect the same?
 
Janiceleong26 said:
No ..sorry..
If actual uncertainty in θ is r, then the percentage uncertainty of θ would be r x100 right?
No, the percentage uncertainty is 100x fractional uncertainty.
 
haruspex said:
No, the percentage uncertainty is 100x fractional uncertainty.
What's the difference between fractional uncertainty and fractional error?
 
  • #10
Janiceleong26 said:
What's the difference between fractional uncertainty and fractional error?
Sorry, I didn't notice I had switched from uncertainty to error. For the purposes of this question it makes no difference.
So in your post #5, you have that if the fractional (or percentage) uncertainty in x is r then the fractional (or percentage) uncertainty in theta is r.
Can you see how that conflicts with A?
 
  • #11
haruspex said:
Sorry, I didn't notice I had switched from uncertainty to error. For the purposes of this question it makes no difference.
So in your post #5, you have that if the fractional (or percentage) uncertainty in x is r then the fractional (or percentage) uncertainty in theta is r.
Can you see how that conflicts with A?
Ohhhh...is it because the percentage uncertainty would be the same for all values of θ, but the uncertainty itself varies?
 
  • #12
Janiceleong26 said:
Ohhhh...is it because the percentage uncertainty would be the same for all values of θ, but the uncertainty itself varies?
Yes.
 
  • #13
haruspex said:
Yes.
Thanks
 
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