Relation between torque and speed

[PhysicsBegner]

Hi Everyone, It is said that speed is inversly propotional to torque ( in Dc motors or a crank shaft powered by engine). I understand that torque is a twisting moment that makes the shaft to rotate, if no torque is applaid then shaft won't rotate. With this context; it is hard for me to understand how we say torque is inversly propotional to speed logically, although a simple math (from power calculation formula) would say they are inversly propotional.
Could anyone help me in this?

 

[rcgldr]

In some electrical motors, there's is a range of rotational speed where power output is nearly constant, where torque decreases as rotational speed increases. This is generally not the case with (fuel consuming) engines. Generally the torque curve versus rpm is a convex curve, with a peak usually near the upper range of it's maximum rotational speed, and power increases as rotational speed increases until very near maximum rotational speed.

 

[PhysicsBegner]

So is it not valid to we make a generic statement that speed is inversly propotional to torque? And does it only applies to certain cases?