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If two quantities have the same dimensions, do they represent the same physical content then?

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  • $\begingroup$ What do you mean by "physical content"? A brick and an ice cream tub may have the same length but very different physical content. $\endgroup$ – Guy Inchbald Mar 27 '20 at 14:05
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Not really. Energy and torque, for example, both have the same units but are very different physical quantities. Energy is conserved, torque is not. Energy is a scalar, torque js a vector. They are very separate concepts despite having the same units. The same is true of angular momentum and action. Angular momentum is a conserved quantity, whereas action is a functional of the path a system takes that is always minimised. Having the same units doesn't show similarity between quantities in every case.

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