Torque: the turning effect of a force

What torque is

• Torque (also called the moment of a force) is the turning effect of a force about a pivot.
• A force produces a turning effect whenever its line of action does not pass through the pivot.

$$\tau = Fd$$

• $\tau$ — torque, measured in newton metres (N m)

• $F$ — the force applied (N)

• $d$ — the perpendicular distance from the pivot to the line of action of the force (m)

• Torque is not measured in joules, even though N m looks like the unit of energy. Always write N m for a torque.

The perpendicular distance is what matters

• $d$ is measured at right angles from the pivot to the line along which the force acts — not simply the length of the object.
• If the force is applied at an angle, the perpendicular distance is shorter than the distance to the point of application, so the torque is smaller.
• The largest torque for a given force and length comes from applying the force at $90°$ to the lever arm.
• This is why:
  • a longer spanner loosens a tight nut more easily — bigger $d$, bigger torque for the same push,
  • a door handle is placed far from the hinges — the same push gives a much larger torque,
  • pushing a door near its hinges barely moves it, even hard.

Direction: clockwise and anticlockwise

• Torque is a turning effect, so its "direction" is either clockwise or anticlockwise about the stated pivot.
• Decide which way each force would turn the object if it acted alone.
• Label each torque clockwise or anticlockwise before adding anything.
• The net torque is the difference between the total clockwise and total anticlockwise torques, acting in the direction of the larger.

Working out a torque

• Identify the pivot — it is usually stated, and if not, it is the hinge, axle or point of support.
• Find the perpendicular distance from the pivot to the line of the force.
• Multiply: $\tau = Fd$.
• State the direction: clockwise or anticlockwise.