How does torque affect speed?

Hint : We know that torque is related to the angular acceleration and the rotational inertia of a body performing rotational motion. It is actually a force that causes a body to rotate about a defined axis. However, we can now see how it is related to the speed of a rotating body as the speed of a body is the measurement of how fast or slow the body is spinning.

Complete step-by-step solution:
Here, we shall under the relation between the torque and speed of a rotating body with the help of an example of a motor which is designed to rotate about its axis.
The three factors that determine the type of work a motor can produce are speed, torque and horsepower. Speed is defined as how fast a motor performs its work. The typical units for measurement of rotational speed are revolutions per minute or rpm. Work is defined as a force applied over a distance. In case of flywheels and motors, this work is called torque. It is the special type of work that causes rotation. Torque occurs when a force acts on a radius. Its unit is Newton meter.
The speed (in rpm), horsepower (HP) and torque $\left( \tau \right)$ are related as:
$\tau \propto \dfrac{HP}{rpm}$
$\Rightarrow \tau \propto \dfrac{1}{rpm}$
Therefore, the torque is inversely proportional to speed, that is, as the torque increases, the speed decreases and vice-versa.

Note:
Horsepower is defined as the rate at which work is being accomplished. Years ago, before machines or motors were invented, most work was accomplished manually with the help of horses. It was estimated that one horse could accomplish approximately $24445Nm$ of work per minute and thus the term horsepower was born.