Yes, Principles of Moments are extensively used in the study of LEVERS.
If you recall the subject of levers, it has three main features, a fulcrum and two arms. On one arm load is applied and on other arm the load is applied. So , we have to calculate moments due to tha applied Force. And, we have to calculate the moments at the load end. Remember all moment are calculated about/ with respect to the Fulcrum.  Hence, in study of Levers, the knowledge of the concept of Moments is very important and useful.