Division of a physical quantity

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SUMMARY

The discussion centers on the interpretation of division in the context of physical quantities, specifically using examples like angular displacement (theta) defined as arc length divided by radius, and voltage defined as work divided by charge. Participants emphasize that these relationships represent ratios rather than simple divisions, highlighting that as one quantity increases, the corresponding ratio changes. The conversation clarifies that physical quantities can be divided into meaningful units, such as apples per person, which illustrates the concept of ratios in practical terms.

PREREQUISITES
  • Understanding of basic mathematical operations, particularly division.
  • Familiarity with physical quantities and their units, such as arc length and radius.
  • Knowledge of voltage as a physical quantity defined by work and charge.
  • Concept of ratios and relationships in mathematics and physics.
NEXT STEPS
  • Explore the concept of ratios in physics, focusing on angular displacement and its applications.
  • Research the relationship between work, charge, and voltage in electrical engineering.
  • Study the implications of unit analysis in physical quantities and their divisions.
  • Learn about dimensional analysis and its role in understanding physical relationships.
USEFUL FOR

Students and professionals in physics, engineering, and mathematics who seek to deepen their understanding of how division applies to physical quantities and the significance of ratios in these contexts.

akashpandey
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TL;DR
Division of normal numbers makes sense but what does division of two physical quantity mean.
As we all know that division simply means how many parts of the whole we have (or splitting into equal parts)
1)Example:- if we have 12 apples and there are 3 people so each will get 4 apples right. Easy!
Now my question is how does this definition makes sense in term of physical quantities ?
2)Example:- theta= arc length/radius
So according to first example i say that theta mean number of radiuses in given arc length ?
similarly what can we say about voltage=work/charge ?
 
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Do you find it strange that we talk about speed as miles per hour (or km per hour)?
 
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akashpandey said:
As we all know that division simply means how many parts of the whole we have (or splitting into equal parts)
1)Example:- if we have 12 apples and there are 3 people so each will get 4 apples right. Easy!
Now my question is how does this definition makes sense in term of physical quantities ?
I just want to point out that apples and persons are perfectly valid physical quantities. So 12 apples / 3 persons is 4 apples/person. That quantity with units of apples/person is a physical quantity representing the number of apples each person has. So you seem to already have an understanding of division of quantities with units.
 
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anorlunda said:
Do you find it strange that we talk about speed as miles per hour (or km per hour)?
No,but Is my second example valid if i say it according to definition of division that is
Theta means how many part of radiuses are there in the arc length ?
 
akashpandey said:
No,but Is my second example valid if i say it according to definition of division that is
Theta means how many part of radiuses are there in the arc length ?
Sorry, I don't understand what you are trying to ask.

If A=B/C then C=B/A. So what?
 
akashpandey said:
...
Now my question is how does this definition makes sense in term of physical quantities ?
2)Example:- theta= arc length/radius
So according to first example i say that theta mean number of radiuses in given arc length ?
similarly what can we say about voltage=work/charge ?
I like calling these cases ratios or relationships rather than divisions.
As the value of arc length increases and/or radius decreases, the value of theta is greater, and vice-versa.
As the value of work increases and/or charge decreases, the value of voltage is greater, and vice-versa.
 

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