Have you tried stopping it while the motor is running?

I usually use a rolled up newspaper or a broom (the end with the bristles not the handle) to stop the fan if it stops easily and especially if it takes a second or so to speed back up when released its toast.

Just watching it spin isn't going to tell you if its working right or not.

A correctly working mechanical fan clutch on bmw's will pull enough air across the condenser to cool it enough to make the a/c work correctly.

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Just BMW's - All cars and trucks was two pages long
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Aftermarket E53 Radio Install