Torque

Torque of a single force

• The torque of a force $F$ about an axis is given by: $$\tau = Fr$$
• Where: $\tau$ = torque (N m), $F$ = applied force (N), $r$ = perpendicular distance between the axis of rotation and the line of action of the force (m).
• Think of a cyclist pushing down on a pedal. The torque on the chain ring depends on the magnitude of the force and the length of the crank arm.

Torque of a couple

• When two equal and opposite forces act at different points on an object, this is called a coupleA pair of equal and opposite forces whose lines of action do not coincide. A couple produces rotation without any linear acceleration..
• The torque of a couple is the sum of the moments produced by each of the forces. For a steering wheel of radius $r$: $$\tau = (F \times r) + (F \times r) = 2Fr$$
• Crucially, the forces are equal and opposite, so the resultant force is zero. This means the object rotates but does not accelerate linearly.
• Due to Newton's Second Law ($F = ma$), a steering wheel under a couple rotates with constant angular speed but remains in the same location.

Worked example: grinding wheel

• A grinding wheel has a diameter of 0.13 m. A tangential force of 12.0 N acts on the edge.
• The radius is $r = \frac{0.13}{2} = 0.065$ m.
• Therefore: $\tau = Fr = 12.0 \times 0.065 = 0.78$ N m.