Dots on physics equations. What do they mean?

In summary, when there is a dot above an equation, it signifies the derivative with respect to time. Two dots above a variable usually mean the second derivative with respect to time, while one dot on the side is most likely a punctuation mark. The notation "f prime" and "f double prime" may also be used for first and second derivatives, respectively. The symbol "x =" is often used to represent the derivative and a period at the end of a sentence should not be confused with a derivative notation. Different units can be used to determine the type of derivative being represented. In the thread, there was a debate about the meaning of a dot on the side, but it was concluded that it was most likely a punctuation mark.
  • #1
epislon58
49
1
So when there is a dot above the equation it means with respect to time. What does it mean if there are two on the top or one on the side?
 
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  • #2
Two on top of a variable usually mean the second derivative with respect to time.
"One on the side" - can you give an example?
 
  • #3
epislon58 said:
So when there is a dot above the equation it means with respect to time. What does it mean if there are two on the top or one on the side?

For future reference, always provide context and sources when you ask something like this.

Zz.
 
  • #4
That is a shorthand of writing the derivative. Two dots above would mean double derivative.

One on the side - I don't recall that one.

PS. 0405, 0406, 0408 and they all showed up with my post not before
 
  • #5
epislon58 said:
So when there is a dot above the equation it means with respect to time. What does it mean if there are two on the top or one on the side?

One dot on top usually means the first derivative with respect to time (that is, speed), two dots on top the second derivative with respect to time (that is, acceleration).

A dot on the side? Show us an example of what you mean and you'll get a better answer.
 
  • #6
perhaps the dot on the side - he is referring to f prime and f double prime - only thing i can think of, only it's not a dot.
 
  • #7
This is what I am talking about.
 

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  • #8
I think that is a punctuation mark. Or a misplaced time-derivative point.
 
  • #9
Well it so the Euler Lagrange equation. Is it suppose to be there ?
 
  • #10
That's hard to tell from the RHS only, as both derivatives (with and without dot) are interesting.
You can check the units to find it out.
 
  • #11
This is the entire equation
 

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  • #13
Thank you good sir.
 
  • #14
it's just derivative wrt time


.
x = dx/dt
= lim: t→0 in x/t
 
  • #15
namanjain, OP is talking about the second dot.
That's just a period marking the end of the sentence.
 
  • #16
CompuChip said:
namanjain, OP is talking about the second dot.
That's just a period marking the end of the sentence.

ohh! sorry read half of the first sentence
well 2 on top means: ..
x =
d2x
______________
dt2

second derivative

eg if
x=t8 e(t2)

a = d2x
______________
dt2

get answer using wits,(:tongue: it's short)

aNs

a= 56t6e(t2) + 34t8e(t2) 4t10e(t2)
 
Last edited:
  • #17
namanjain please read the full thread, you are not adding anything new here.
 
  • #18
mfb said:
namanjain please read the full thread, you are not adding anything new here.

then i suppose discussion is over, thank you
 
  • #19
Over means over, thread closed.
 

1. What do the dots on physics equations represent?

The dots on physics equations are called the "dot product" and represent the mathematical operation of multiplying two vectors together. It is also known as the scalar product, as it results in a scalar quantity (a single number) rather than a vector.

2. How is the dot product calculated?

The dot product is calculated by multiplying the corresponding components of two vectors and then adding them together. For example, if vector A has components (a1, a2, a3) and vector B has components (b1, b2, b3), then the dot product of A and B would be (a1b1 + a2b2 + a3b3).

3. What is the significance of the dot product in physics equations?

The dot product is important in physics equations because it allows us to calculate the work done by a force, the angle between two vectors, and the projection of one vector onto another. It also helps determine if two vectors are parallel or perpendicular to each other.

4. Can the dot product be negative?

Yes, the dot product can be negative. This occurs when the angle between two vectors is greater than 90 degrees. In this case, the dot product is negative because the vectors are pointing in opposite directions.

5. How is the dot product related to the cross product?

The dot product and the cross product are two different mathematical operations involving vectors. The dot product results in a scalar quantity, while the cross product results in a vector quantity. The dot product is used to find the angle between two vectors, while the cross product is used to find the perpendicular vector to two given vectors.

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