# Physics Tutorial 6.9 - Torque Revision Notes

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6.2Torque

In these revision notes for Torque, we cover the following key points:

• What is torque?
• Where does torque change from the moment of force?
• How torque is calculated?
• What is the positive direction of torque?

## Torque Revision Notes

By definition, "Torque is a non-zero resultant moment of force usually produced by a single force or a couple of forces that help each other when trying to rotate a system around a fixed point."

Torque can be either produced by a single force of by a couple of forces as long as they are able to create rotation in the system. The meaning of torque is very close to that of moment of force. The most important difference between these two concepts lies in the fact that torque is a movement effect whereas moment of force is a static effect. This means torque is used where there is rotation involved whereas moment of force is used where there is no rotation (when there is equilibrium).

Examples of torque involving a couple of forces include:

1. Rotating the steering wheel of a car,
2. Rotating the handle bar of a bike,
3. Two men rotating a grinding mill, etc.

Other examples of torque but which involve the use of a single force include:

1. Pushing a door as it swings on its hinges when pushed,
2. Turning the key,
3. Turning the dood knob, etc.

Both Moment of Force and Torque have the same unit i.e. N-m but The equation of torque for a single force applied is:

τ = r × F

where r is the distance from the turning point (usually the radius of a circle), and F is the perpendicular force to the bar (line of action) or the tangent force used at that specific point of the circle.

The scalar equivalent of the above equation is

|τ| = |r| × |F| × sin θ

where θ is the angle between the axis of rotation and the force applied.

As for the torque of a couple, we obtain the following equation:

τ tot = r 1 × F 1 + r 2 × F 2

When the couple of forces is used to rotate a kind of wheel (such as a steering wheel), we have r1 = r2 = r

As for the signs of the directions of rotation, anticlockwise is taken as positive [clockwise is negative].

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