Final answer:
A variable-speed head allows continuous speed adjustment often through electronic control, while a step-pulley head has fixed speed settings that require manual belt adjustments. Calculations to compare performance at different speeds would involve torque and angular momentum, requiring measurements of rotational speed, radius, and moment of inertia.
Step-by-step explanation:
The difference between a variable-speed head and a step-pulley head lies in the mechanism they use to change the speed of the tool. A variable-speed head allows for continuous adjustment of speed, providing a wide range of speeds that can be easily changed while the machine is running. The speed changes are typically made by turning a dial or electronically controlling the motor speed.
This allows for greater flexibility and precision in operations that require varying speeds. On the other hand, a step-pulley head requires the machine to be stopped to manually adjust the positioning of the belts across a series of pulleys to change the speed. This design has distinct speed settings, known as steps, and you can only select from these predefined speeds. Step-pulley heads are more simplistic and may be less expensive, but they offer less convenience compared to variable-speed heads.
When discussing power tools and their speed mechanisms, such as in electric screwdrivers or tabletop fans, you would look into torque and angular momentum calculations to differentiate their performance at varying speeds. Measurements needed would include the rotational speed of the tool (usually in revolutions per minute or RPM), the radius of the rotating element, and potentially the force applied if calculating torque.