Torque (Moment of a Force)

Turning effect of a force about an axis. Covers: Definition of Torque and Calculating Torque.

General idea of the topic

The moment of a force, or torque, measures the ability of a force to make a body rotate about a point or an axis. It is the cross product of the position vector with the force, so it depends on where and in what direction the force is applied, not only on its magnitude.

The topic defines the moment and its direction, perpendicular to the plane formed by r and F, and teaches how to compute it with three equivalent ways: force times arm, tangential force times distance and the cross product by components.

What you will truly understand

By the end you will be able to compute the magnitude, direction and sign of the moment of a force, add moments of several forces and recognize when a moment is zero.

You will also know why a force directed toward the axis does not produce rotation and why a long wrench makes it easier to loosen a nut.

Recommended learning route

1. Definition of Torque: moment as a cross product, its direction by the right-hand rule and its units.
2. Calculating Torque: practical computation using the lever arm, the tangential component and Cartesian components.

Physical criterion you must acquire

The essential criterion is to use only the component of the force perpendicular to the arm, or equivalently the arm perpendicular to the line of action. The moment vanishes if the force passes through the axis or is parallel to the position vector, and the total moment is the vector sum of those of each force.

Connection with real problems

• wrenches, screws and screwdrivers.
• doors, hinges and cranks.
• bicycle pedals and steering wheels.
• levers and scales.

Final goal of the topic

The final goal is to compute the moment of any force about an axis with confidence and use it as the starting quantity of rotational dynamics.