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Physics/dimensional analysis


QUESTION: if all terms in an equation have same units, will they have same dimension? if dimensions are same will terms have same unit?

ANSWER: Yes to the first, no to the second.  the dimensions on both sides of an equals sign have to be the same.  Such as work = force times acceleration

---------- FOLLOW-UP ----------

QUESTION: can you make it more clear by an example with equation

I wrote the equation wrong.
Force = mass times acceleration = (kg)(m/s^2)
the unit for force is the Newton which is dimensionally kgm/s^2
Work = force times distance = Newton-meter
the unit for work (or energy) is a Joule which is dimensionally kgm^2/s^2

I just gave you two examples where the dimensions are the same on both sides of the equation.


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Richard J. Raridon


I can answer most questions in undergraduate physics courses, including electricity and magnetism, atomic and nuclear, mechanics and optics.


I have taught undergraduate physics courses

Sigma Xi, AAAS, SE section of APS

BA in math, MA in physics, PhD in physical chemistry

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