Problem using UnitConvert

Question

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.

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

Answer 1

"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"]

Answer 2

In MMA 13.3, the selected answer no longer works. The following uses the newer RevolutionUnit unit dimension. Not sure when it changed.

UnitConvert[Quantity[335, "Kilowatts"] /
  UnitSimplify[Quantity[1, "FullAngle"] Quantity[3000, "Revolutions"/"Minutes"], 
  UnityDimensions -> {"RevolutionUnit", "AngleUnit"}], 
  "Newtons" "Meters"
]

(* Out[] *)
Quantity[3350/Pi, "Meters"*"Newtons"]