Final answer:
The best method for producing measurable torque is placing known masses on one end of a seesaw to study the relationship between angular momentum, torque, and time.
Step-by-step explanation:
The question concerns the production of measurable amounts of torque on a system, with the intent of testing the relationship of the system's angular momentum, the applied average torque, and the time duration of the torque application.
The best method among the given options for creating a scenario where torque is consistently measurable and controllable would be placing known masses on one end of a seesaw.
This approach allows for precise calculations of torque since the mass (m), the force due to gravity (F), and the distance from the pivot point (d) can be accurately known, enabling consistent replication of the experiment with different variables to observe how torque impacts the angular momentum during a specified time.
The best way to produce measurable amounts of torque on a system to test the relationship between the angular momentum, average torque, and time is by hanging known masses from a string that is wound around a spool suspended horizontally on an axle.