Torque is the technical term for a "twist". A mechanical engineer will instead call a torque a [b]moment[/b]. This is useful to know if you are going into engineering. We will use the Greek lower case tau (sounds and looks like our 't') to denote torque. Since torque is a vector, it will be denoted [math]\vec\tau.[/math]

To twist something requires leverage. Think about twisting a door knob, for instance. Do you think it will be easy if the knob has a very small radius? Think about loosening a bolt with a wrench. The longer the wrench the more effective your efforts and the larger the torque. The definition of torque takes both the leverage and the force acting on that lever into account:[br][br][center][math]\vec\tau = \vec{r}\times\vec{F}.[/math][/center]

In this definition the first vector [math]\vec{r}[/math] starts at the point of rotation and ends at the point where the force [math]\vec{F}[/math] is applied. It plays the role of the lever arm. On a wrench, for instance, this vector would start at the bolt or nut and extend to the point on the wrench where your hand is pushing or pulling. Due to the nature of the cross product, your intuition is likely verified by the fact that for a given lever arm and force, that the torque is maximized when the two vectors are orthogonal. The equation and life experience also indicate that if the vectors are parallel or anti-parallel, you will have no ability to turn a nut or bolt. [br][br]The conventions can be seen in the graphic below. The torque vector - due to the nature of the cross product - will always be perpendicular to the plane defined by the two vectors [math]\vec{r}[/math] and [math]\vec{F}.[/math] In this case that's either outward from the screen or inward toward the screen.

The effect of a torque is to induce an angular acceleration in what is known as Newton's second law for rotations:[br][br][center][math]\sum\vec{\tau}=I\vec{\alpha}.[/math][/center]