I had a look at a huge windmill and was wondering how fast the blades are spinning. Obviously, the distance the blades make is different on the outside than on the inside. Is the speed of a rotating object always measured in rpm and not in mph?
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If you’re doing any serious math related to rotation, radians per second is the best. Absolutely anything else will require some conversion factor. That’s not to say they aren’t common. For instance, the number of poles in an induction motor is typically 120*f/s where frequency is in Hz and speed is in rpm. But that 120 factor is to make the formula work with rpm.
RPM is often used because it’s a more familiar number to work with. If I say something is spinning at 50.26 rad/s, that is going to be tough to work with mentally. But convert that to 480 RPM and you can already have an idea how fast that is. You know it’s slow compared to an engine, but maybe pretty quick if it’s a carnival ride. You can also use your multiplication tables to get to 8 rotations per second which is even more understandable to a human.
The one and only reason anyone should ever report a rotational speed in distance per time (like miles per hour) is a shock value. A news story might use it because it sounds crazy or deadly or impressive and they know it’ll get more clicks. But no engineer, mathematician, mechanic, or really any industry professional will ever use mph to represent rotational speed.
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