I have an aircompressor but I would like to add a permissive start for an air cooler when the aircompressor start. Is it ok to use the auxiliary contact of the motor starter? or is there another way? pls advise.
The Best Approach would be to use a feedback which tells you if the air compressor has actually started working. But if you dont have that luxury then the choice you have mentioned can be used.
If the air cooler is to refrigerate the air and 'Dry' the output from your air compressor.
Then you may need to re-think what you are trying to achieve.
It will work with your original thought but, takes a long time to reach the DEW point so water will be passed through the lines.
Consider to prestart the cooler and after a while, auto start the compressor.
I can't see any reason why your original thought wouldn't work; it should be fine as long as the rating of the auxiliary contact is sufficient to control the switching load.