When I run a device with a 15 amp motor, why doesn't the 15 amp breaker trip when I flip on a light on the same circuit?
The motor rating on the saw is the FLA (full load amperage). With the saw running without a load (cutting the material is the load) the saw will not be pulling the full load amperage. Many small motors are rated at peak draw (closed to locked rotor current) the motor never draws this amount until the motor is almost stalled. The "phony FLA" is used on air compressors, vacuum cleaners, table saws and many hand tools to get the buyer to pick that manufacturer If the actual current draw is measured you might find the saw is only drawing 1/2 the current listed on the name plate. A true 120v 1 HP motor FLA is listed as 16 amps This size motor would trip a 15 amp breaker (on start up even tripping a 20 amp breaker) because the starting current is usually 2-4 times the FLA for the time required to get to speed. I would doubt that your breaker is defective but the only way to tell with certainty is to measure the actual current on the branch circuit.