Adding units and counters

  • #1
HappyFeynman
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Homework Statement:
In class, we had determined that radians are a form of a count of distance in terms of radius units. We stated this is different from other units such as m, s, etc. I am having an issue in determining whether two values can be added. Lets say we have the equation (6.7 rad^2 * m) + (3 m) = z. Since we defined radians as a count of distance, we can put it in terms such as 1 rad^2 = m^2 / m^2 = 1, so it is dimensionless. Because of this, can I add the two values to simply state that z= 9.7 m?
Relevant Equations:
1 rad^2 = m^2 / m^2 =1
(6.7 rad^2 * m) + (3 m) = 9.7 m
 

Answers and Replies

  • #2
BvU
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  • #3
haruspex
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You might find this interesting: https://www.physicsforums.com/insights/can-angles-assigned-dimension/.
The bottom line is that rad2 is certainly dimensionless, but if you find you are adding terms that have a mix of radians to an even power and radians to an odd power then you have very likely gone wrong. E.g. energy, ##ML^2T^{-2}##, cannot equal angular momentum, ##ML^2T^{-2}\Omega##, where ##\Omega## represents the 'angular' dimension.
 

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