This doesn't seem to be an IT question - but here goes.....the only way to test the pully is to test the pully.
Remove whatever material may be on the pully and try to turn. If this is a simple tension pully - you should have no problem. If it is driving something else - it may not be able to turn.
Once cleaned - you should replace the belt and see if there is any wobble or vibration in the pully (or other areas). If so - you will likely need to replace the dammaged part.