How to read a specific type of dimensional analysis

In summary, the notation "for energy ... ML^2 T^{-2}" is read as "mass times length squared divided by time squared" and in SI units, it is equivalent to kilograms times meters squared per second squared, which is the unit for energy, or joules.
  • #1
help1please
167
0


In some work I have been following, I keep seeing notation like:

for energy ... [tex]ML^2 T^{-2}[/tex]

How is this supposed to be read? I understand this is using mass, length and time, but what is it saying? Would I be right in thinking it says

''mass times length squared divided by time squared?''

As soon as I understand that, I think I will understand how to read this kind of notation

Thanks in advance!
 
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  • #2
hi help1please! :smile:
help1please said:
for energy ... [tex]ML^2 T^{-2}[/tex]

How is this supposed to be read? I understand this is using mass, length and time, but what is it saying? Would I be right in thinking it says

''mass times length squared divided by time squared?''

exactly! :smile:

(and that tells you that in SI units it will be in kg m2 s-2, ie J)
 
  • #3
Thank you very much!
 

1. How do I read and interpret dimensional analysis?

Dimensional analysis is a method used to convert units of measurement and solve problems involving physical quantities. It involves using conversion factors and unit cancellation to ensure that the final answer has the correct units.

2. What are the steps to perform dimensional analysis?

The first step is to identify the given quantity and the desired quantity. Then, list the conversion factors needed to convert between the two units. Next, set up the problem using a conversion factor for each step and cancel out the unwanted units. Finally, multiply all the numbers together to get the final answer.

3. Can dimensional analysis be used for any type of unit conversion?

Yes, dimensional analysis can be used for any type of unit conversion as long as the units being converted are equivalent. This means that they measure the same physical quantity, such as length, time, or mass.

4. How can I check if my dimensional analysis answer is correct?

You can check your answer by making sure the units cancel out correctly and checking if the final answer has the correct units. Additionally, you can estimate the answer to see if it is reasonable based on the given quantities.

5. Are there any common mistakes to avoid when using dimensional analysis?

Some common mistakes to avoid include using the wrong conversion factor, not canceling out units correctly, and using inconsistent units throughout the problem. It is also important to pay attention to the direction of the conversion, as some conversion factors may need to be inverted.

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