Torque

A torque is when we have a couple acting on an object, to rotate it.

It basically measures the magnitude of the turning effect (moment) caused by a couple.

Because it’s a rotation, it must have a moment!

Calculating torque

The turning effect is the sum of both moments in the couple.

• For example, if we have a couple with two forces:
  • A 5N force 2m away from the pivot, clockwise
  • A 5N force 3m away from the pivot, clockwise
• …then we know that the first moment must be 5\times2=10Nm and the second moment must be 5\times3=15Nm.
• Adding them together, we get 10Nm+15Nm=25Nm, so our torque is 25Nm.

We could also have done this by simply multiplying the force by the distance between the couple’s forces:

• 2m+3m=5m
• M=5N\times5m=25Nm
• That gives us the same torque of 25Nm.

Torque formula

We can use that to write a formula for torque, which looks very familiar:

\text{torque}=Fd

Where:

• \text{torque} is the combined moment of the forces
• F is the magnitude of a single force (one of the components of the couple)
• d is the distance between the couple’s forces

Units of torque

Torque is just the combined moment, so it’s measured in the same way: using newton-metres.

Calculations

Two forces of 8N act clockwise on a metal bar. The forces are 9m away from each other. Find the turning effect.

• M=Fd
• M=8N\times9m
• M=72Nm

The torque on a stick is 7Nm. The perpendicular distance between the couple is 3.5m. Find the sum of the magnitudes of the forces acting.

• M=Fd
• F=\frac Md
• F=\frac7{3.5}
• F=2N
• The force of one is 2N
• So the combined force of both components of the couple must be 2\times2=4N
• Answer: 4N

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