Torque and Angular Momentum

For a complete discussion of torque, and examples of torque calculation, click here.

For a discussion about torque static equilibrium, click here.

The direction of the torque vector is given by the right hand rule and the vector product:

t = r x F.

The directions of angular velocity w and angular momentum L = Iw are also determined by the right-hand rule: rotate the fingers of the right hand around the wheel in the direction of rotation, and the thumb will point along the axis of rotation in the direction of the w or L.

When L increases, it does so under the influence of an angular impulse tDt (analogous to impulse J giving rise to linear momentum p). The torque vector will cause the speed of rotation of a wheel to increase when it points in the same direction as angular velocity; conversely, the wheel will slow down when t points opposite to w.

What happens when torque points at right angles to angular velocity ? Recall that when a force acts at right angles to linear velocity, we call the force centripetal and the resulting motion is circular: velocity changes in direction, but not magnitude. In rotation, an analogy exists:


The vector cross product is used to define the direction of torque, and then this direction can be compared to the direction of angular velocity to predict what will happen next. Click here for an example.

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