Why the Inconsistent Use of Δ in Physics?

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In summary, the symbols used in physics notation, such as Δ and d, serve different purposes and are used in different contexts to represent either finite or infinitesimal changes. The deltas are used in the conservation of energy formula to denote a change in energy, while the d represents a derivative. The symbols are used to prepare students for practical problem-solving and may not always represent infinitesimal changes. The use of these symbols depends on the specific problem at hand and different problems may require different approaches.
  • #1
Bullwinckle
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Hello,

Sometimes in introductory physics, I see this:

After defining P as the momentum, we show: dP/dt = F

Then, later, I see this

ΔL = mv1 - mv2

So my question is really simple: WHY is there no consistency? Why do we sometimes use the Δ symbol? Is there something about how the definition is being applied (small change but not infinitesimally small), that makes the books switch back to Δ

I see it here, too (where U is the potential energy in a non-dispersive system):

ΔK.E. + ΔU = 0

Is there an APPLIED (as, say, in engineering) advantage to using the above, and not: K.E. + U = constant which, as I see it, is more theoretically precise.
 
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  • #2
The d denotes the derivative. In a less rigorous sense, it usually denotes an infinitesimally small difference, as opposed to delta, which is any finite difference. The deltas are used in the conservation of energy formula because energy itself has not inherent meaning--it is the change of energy that's important. It makes no sense to say K.E + U = 0. Using the deltas tells us that there is no change in the total energy of the system (some of it might have converted between forms, but the total change is 0).
 
  • #3
axmls said:
The deltas are used in the conservation of energy formula because energy itself has not inherent meaning--it is the change of energy that's important. It makes no sense to say K.E + U = 0. Using the deltas tells us that there is no change in the total energy of the system (some of it might have converted between forms, but the total change is 0).

Thank you
 
  • #4
axmls said:
The d denotes the derivative. In a less rigorous sense, it usually denotes an infinitesimally small difference, as opposed to delta, which is any finite difference. The deltas are used in the conservation of energy formula because energy itself has not inherent meaning--it is the change of energy that's important. It makes no sense to say K.E + U = 0. Using the deltas tells us that there is no change in the total energy of the system (some of it might have converted between forms, but the total change is 0).

Oh, one more thing...

Are you saying that books use this:

ΔL = mv1 - mv2

Simply to prepare students to solve problems over a finite time difference that is not infinitesimally small?

So, here, the Δ is being used for a PRACTICAL purpose?
 
  • #5
We're often concerned with the change in quantities--not necessarily infinitesimal changes. The change in energy would be the obvious one. These aren't (usually infinitesimal). For instance, if we slide a block down a frictionless incline, we may be interested in the change in kinetic energy between the time at which the block is on top and the time at which it's on the bottom.

So really, different problems require different approaches. It's sometimes the case that we end up taking a limit as these differences go to 0, in which case we end up with a derivative or integral (somewhat non-rigorously), but again, this all depends on context.
 

1. Why is the symbol Δ used in physics?

The symbol Δ is used in physics to represent a change or difference in a quantity. It is derived from the Greek letter delta, which has been traditionally used to represent change in mathematics and science.

2. Is Δ always used in the same way in physics?

No, the use of Δ in physics can vary depending on the specific context and equations being used. In some cases, it may represent a change in position or displacement, while in others it may represent a change in velocity or acceleration.

3. Why is Δ sometimes used instead of the letter d?

In physics, the letter d is often used to represent a small change in a quantity. However, Δ is used instead to make it clear that the quantity being represented is a change or difference, rather than a specific value.

4. Are there any other symbols that can be used instead of Δ?

Yes, there are other symbols that can be used to represent a change or difference in a quantity. Some common alternatives include the letter delta with a subscript, such as Δx or Δt, or the symbol △.

5. How can I remember when to use Δ in physics equations?

A good way to remember when to use Δ in physics equations is to think about the meaning of the symbol. Remember that Δ represents a change or difference, so it should be used when calculating a change in a quantity, such as displacement, velocity, or acceleration.

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