Moments — Turning Effects of Forces

A force of 20 N is applied 0.5 m from a pivot. Calculate the moment.

$M = F \times d = 20 \times 0.5 = 10 \text{ N·m}$

A child weighing 300 N sits 2 m from the pivot of a seesaw. Where must a 400 N child sit to balance it?

Clockwise moment = Anticlockwise moment

$300 \times 2 = 400 \times d$

$600 = 400d$

$d = 1.5$ m from the pivot.

A door handle is positioned far from the hinge (the pivot) — typically 80 cm away. If you push with 5 N at the handle:

$M = 5 \times 0.8 = 4$ N·m of turning effect.

If you pushed at 10 cm from the hinge instead, you would need $4 / 0.1 = 40$ N — eight times more force for the same turning effect. Architects place handles at the far edge of doors for exactly this reason.

In a wheelbarrow, the wheel acts as the pivot. The load sits close to the wheel; you lift at the handles, which are much further away. A 200 N load placed 0.4 m from the pivot creates a clockwise moment of $200 \times 0.4 = 80$ N·m. You only need to apply $80 / 1.2 = 67$ N at the handles (1.2 m from pivot) to balance it — lifting a 200 N weight with only 67 N of effort. This mechanical advantage is why wheelbarrows are so useful on building sites.

A mechanic needs 30 N·m of moment to tighten a wheel nut. With a short spanner ($d = 0.15$ m): $F = 30 / 0.15 = 200$ N — quite hard to apply. With a longer breaker bar ($d = 0.5$ m): $F = 30 / 0.5 = 60$ N — well within comfortable reach. Racing teams use torque wrenches (calibrated moment tools) to ensure wheel nuts are tightened to exactly the right moment, preventing both under-tightening (wheel loosens) and over-tightening (stud snaps).