Final answer:
The handpiece that can be used with a variety of attachments is referred to as the flexible shaft motor, which is versatile and commonly used in dental and jewelry-making applications.
Step-by-step explanation:
The handpiece that can be used with a variety of attachments is the flexible shaft motor. This type of motor is commonly used in dental and jewelry-making applications because it allows the user to change attachments based on the task at hand, such as drilling, polishing, or grinding. The versatility of the flexible shaft motor makes it a valuable tool, as it can be adapted to a wide range of detailed and precision tasks.