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
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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.