Step 1: Draw a Free Body Diagram: Clearly label all forces (weight, reactions, tensions) and their exact points of application along the body.
Step 2: Identify Distances: Determine the perpendicular distance from your chosen pivot point to the line of action of every force acting on the system.
Step 3: Strategic Pivot Selection: Choose a pivot point that lies on the line of action of an unknown or unwanted force; this makes its moment zero and eliminates it from the equation.
Step 4: Formulate Equations: Write one equation for the balance of forces (e.g., Upward Forces = Downward Forces) and one or more moment equations.
Step 5: Solve Simultaneously: Use the resulting equations to solve for the unknown variables, ensuring that units remain consistent (Newtons and Metres).
| Feature | Translational Equilibrium | Rotational Equilibrium |
|---|---|---|
| Primary Condition | Resultant Force is zero () | Resultant Moment is zero () |
| Physical Result | No linear acceleration | No angular acceleration |
| Reference Point | Independent of position | Must be calculated about a specific pivot |
| Typical Equation |
The 'Zero Moment' Trick: Always look for a point where two or more unknown forces intersect; taking moments about this point will significantly reduce the algebraic complexity of the problem.
Check Your Units: Ensure all distances are in metres and all forces are in Newtons; a common error is using mass (kg) instead of weight () in the moment calculation.
Consistency in Direction: Explicitly state which direction (clockwise or anti-clockwise) you are treating as positive before writing your moment sum.
Sanity Check: If a reaction force at a support is calculated as negative, it usually indicates that the object would actually lift off that support in the given configuration.
The Perpendicular Distance Error: Students often use the distance along a slanted beam rather than the horizontal or vertical distance perpendicular to the force's line of action.
Ignoring the Beam's Weight: Unless a beam is described as 'light', its own weight must be included as a force acting through its centre of mass.
Tilting Misconception: When an object is 'on the point of tilting' about pivot A, the reaction force at any other pivot B becomes exactly zero, not just 'small'.
Pivot Confusion: Remember that while you can take moments about any point, the most useful points are those that eliminate the most unknowns.
