App note: Voltage vs. output speed vs. torque on DC motors

App note from Precision Microdrives about DC motor capabilities and their uses. Link here

Why Change Torque?
The most obvious benefit of varying the torque is to maintain a constant speed when the motor’s load varies, keeping in mind the interdependent nature of speed, torque, and voltage.

Although this example may be outdated, audio cassettes are a great way of explaining how some applications need to vary the torque to match a changing load. As the cassette plays and the audio tape moves from one spindle to the other, the driving motor will experience a change in load. However, the playback must remain at a constant speed throughout – otherwise the audio pitch would be affected.

Why Change Speed?
The ability to vary motor speed whilst maintaining a steady torque is essential to many applications for a variety of reasons.

An example of an application that requires a variable speed and steady torque is an audio CD player as it is commonly observed that the CD will rotate faster at certain points than others. This is because the information is stored in spiralled circular tracks on the disk and the length/circumference of the track is directly proportional to the amount of information stored on them. This means that the speed must be decreased as the laser is reading from the outermost tracks because there is more information per revolution. Inversely, the speed is increased as the laser reads from the innermost tracks as the spiral circumferences are smaller and therefore contain less information per revolution.

from Dangerous Prototypes