How is theta obtained when using torque = F*r*sin(theta)?

[kathyt.25]

Homework Statement

For the equation torque = F*r*sin(theta), is theta obtained from either angle:
F makes with r (or perpendicular component of F makes with r, or the perpendicular component of r makes with F)?

Homework Equations

The Attempt at a Solution

 

[djeitnstine]

Torque can be written as $$\tau = \vec{r} \times \vec{F}$$ so one must measure the angle between r and F.

So find r then measure the angle created by F. So basically we're looking at the perpendicular component of F.
It would make no sense if it was the component of the moment arm r.

 

[PhanthomJay]

I find it best when using T = Frsin theta to use theta as the included angle between F and r, then assign a positive or negative value to it depending on whether the torque is cw or ccw. It is often easier, however, depending on the problem, to calculate torque as the product of the force times the perpendicular distance from the line of action of the force to the point about which you are calculating the torque, with appropriate plus or minus sign.