Definition of a Moment

A moment is the turning effect of a force around a pivot point or axis. It depends on both the magnitude of the force and its perpendicular distance from the point of rotation. The equation for calculating a moment is:

• Measured in Newton-metres ($Nm$).
• For example, applying a larger force or increasing the distance from the pivot increases the moment.

Example Problem Using the Principle of Moments

Given a beam in equilibrium, supported at two points with forces acting at different distances:

1. Identify the pivot and take moments around it.
2. Set the sum of clockwise moments equal to the sum of anticlockwise moments.

Example Calculation:

For the beam below, find $F$ :

• Clockwise Moments = Anticlockwise Moments
• Given:
• $50\text {\ N force at} \ 2 , \text{m}$,
• $35\ N$ force at $3\ m$,
• Unknown $F$ at $3.5 \, \text{m}$ from the pivot $A$.

Key Points

1. Moment: Calculated by force and perpendicular distance to the pivot; a measure of the force's turning effect.
2. Couple: Pair of equal, opposite forces producing rotation without translation.
3. Principle of Moments: For equilibrium, the total clockwise moments must equal the total anticlockwise moments.
4. Centre of Mass: The point at which an object's mass is effectively concentrated, crucial for balance and stability.