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As we know in physics, power = torque * (angular velocity). But when I use UnitConvert to convert a quantity expressing power/(angular velocity) into newton-meters, UnitConvert fails.

result

How can they be incompatible units? How do I deal with it?

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"Revolutions" is not immediately recognized as a special unit. So, preprocess first with UnitSimplify[]:

UnitConvert[UnitSimplify[Quantity[335, "Kilowatts"]/
                         Quantity[3000, "Revolutions"/"Minutes"], 
                         UnityDimensions -> {"AngleUnit"}], "Newtons" "Meters"]
   Quantity[3350/π, "Meters"*"Newtons"]
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