define and apply the moment of a force

Turning Effects of Forces

What is a Moment?

In physics, the moment of a force (or torque) measures how effectively a force can rotate an object about a point or axis. It depends on two key factors:

  • How hard you push – the force \$F\$

  • How far from the pivot you push – the lever arm \$r\$

Mathematically:

\$\tau = r\,F\,\sin\theta\$

where \$r\$ is the distance from the pivot, \$F\$ the force, and \$θ\$ the angle between them. In most classroom problems the force is applied perpendicular to the lever arm, so \$\sinθ = 1\$ and the formula simplifies to \$τ = rF\$.

Analogy: Opening a Door

Imagine you’re opening a door. The door’s hinges are the pivot point. If you push near the hinges (small \$r\$), it’s hard to turn – the moment is small. Push near the handle (large \$r\$), and the door swings easily – the moment is large. The harder you push (larger \$F\$), the faster it opens.

Example Problem

Calculate the moment produced by a 30 N force applied 0.5 m from the pivot.

  1. Identify \$r\$ = 0.5 m and \$F\$ = 30 N.

  2. Assume the force is perpendicular to the lever arm, so \$\sinθ = 1\$.

  3. Use \$τ = rF\$:

  4. \$τ = 0.5\,\text{m} \times 30\,\text{N} = 15\,\text{N·m}\$.

Moment Table

Lever Arm \$r\$ (m)Force \$F\$ (N)Moment \$τ\$ (N·m)
0.254010
0.752015
1.01515

Exam Tip Box

Tip: Always check the direction of the moment. A clockwise moment is usually taken as negative, while counter‑clockwise is positive. This sign convention helps when you set up equilibrium equations.

Remember to use consistent units: \$N·m\$ for moment, \$m\$ for distance, and \$N\$ for force.

Quick Review

  • Moment = \$r\$ × \$F\$ (when force is perpendicular).

  • Units: \$N·m\$.

  • Direction: clockwise = negative, counter‑clockwise = positive.

  • Use the lever arm (distance from pivot) to increase or decrease the moment.