Define the moment (torque) of a force and use the equation
\$\text{Moment (M)} = F \times d_{\perp}\$
where F is the magnitude of the force and d⊥ is the perpendicular distance from the line of action of the force to the pivot (axis of rotation).
Key Concepts
Moment (Torque) – a measure of the turning effect of a force about a pivot.
Perpendicular distance – the shortest distance from the pivot to the line of action of the force; it is always measured at right angles to the force.
Moments that cause rotation in opposite directions are considered opposite in sign (e.g., clockwise negative, anticlockwise positive).
The principle of moments: For a body in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.
Formula Recap
The moment of a force about a pivot is given by
\$M = F \times d_{\perp}\$
Units: Force in newtons (N), distance in metres (m), so moment in newton‑metres (N·m).
Worked Example
Problem: A force of 30 N is applied to a wrench at a distance of 0.25 m from the bolt (pivot). Calculate the moment produced.
Identify the force: \$F = 30\ \text{N}\$.
Identify the perpendicular distance: \$d_{\perp} = 0.25\ \text{m}\$.
Apply the formula: \$M = F \times d_{\perp} = 30\ \text{N} \times 0.25\ \text{m} = 7.5\ \text{N·m}\$.
The wrench exerts a moment of \$7.5\ \text{N·m}\$ about the bolt.
Common Mistakes
Using the slant distance instead of the perpendicular distance.
Ignoring the direction of rotation (sign of the moment).
Mixing units (e.g., cm with N without conversion).
Practice Questions
A door is 0.9 m wide. A force of 15 N is applied at the edge of the door, perpendicular to the surface. What is the moment about the hinge?
A wrench is 0.2 m long. A force of 40 N is applied at an angle of 30° to the wrench. Calculate the effective perpendicular distance and the resulting moment.
Two forces act on a seesaw: 50 N clockwise at 0.6 m from the pivot and 30 N anticlockwise at 1.2 m from the pivot. Determine whether the seesaw is in rotational equilibrium.
Variable Table
Symbol
Quantity
Unit
Typical \cdot alue (example)
\$F\$
Force
newton (N)
30 N
\$d_{\perp}\$
Perpendicular distance from pivot
metre (m)
0.25 m
\$M\$
Moment (torque)
newton‑metre (N·m)
7.5 N·m
Suggested diagram: A lever with a pivot, showing a force applied at a point and the perpendicular distance to the pivot, with arrows indicating clockwise and anticlockwise moments.
Summary
The turning effect of a force is quantified by its moment, calculated as the product of the force magnitude and the perpendicular distance from the pivot. Remember to keep units consistent and to consider the direction (sign) of each moment when solving equilibrium problems.