Turning Effects of Forces

• Rotational Equilibrium: For an object to be in a state of rotational equilibrium (not rotating or rotating at a constant angular velocity), the sum of the moments acting on it must be zero.

• The Principle: When an object is in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about that same point.

Equilibrium Condition: $\sum M_{\text{clockwise}} = \sum M_{\text{anticlockwise}}$

• Application: This principle allows for the calculation of unknown forces or distances in balanced systems, such as seesaws, cranes, or structural beams.

• Center of Gravity (CG): The single point through which the entire weight of an object appears to act. For a uniform object, this is located at its geometric center.

• Stability Criteria: An object is stable as long as the vertical line of action from its center of gravity falls within its base of support. If the CG moves outside the base, a resultant moment is created that causes the object to topple.

• Factors Affecting Stability: Stability is increased by lowering the center of gravity (e.g., placing heavy components at the bottom) or widening the base of support.

• Moment vs. Pressure: While both involve force, pressure is force distributed over an area ($F/A$), whereas a moment is force acting at a distance to create rotation.

• Identify the Pivot First: Always start by clearly marking the pivot point. In complex problems with multiple supports, you can often choose a pivot at the location of an unknown force to eliminate it from the moment equation (since $d=0$).

• Check Units: Ensure all distances are converted to metres (m) and forces to Newtons (N) before calculating. A common mistake is using centimetres, resulting in Ncm instead of the standard Nm.

• Directional Consistency: Explicitly label each moment as 'CW' (clockwise) or 'ACW' (anticlockwise). Sum them separately before setting them equal to each other.

• Sanity Check: If a small force is balancing a large force, the small force must be significantly further from the pivot. If your calculation shows otherwise, re-check your distance measurements.