State the equation for magnitude of torque and explain various cases of angle between the direction of vectors r and F.

Magnitude of torque, τ = r F sin θ where θ is the smaller angle between the directions of \(\overrightarrow{r}\) and \(\overrightarrow{F}\).

Special cases:

1. If θ = 90°, τ = τmax = rF. Thus, the force should be applied along normal direction for easy rotation.

2. If θ = 0° or 180°, τ = τmin = 0.

Thus, if the force is applied parallel or antiparallel to \(\overrightarrow{r}\), there is no rotation.

3. Moment of a force depends not only on the magnitude and direction of the force, but also on the point where the force acts with respect to the axis of rotation. Same force can have different torque as per its point of application.