9231 · 3.2
Equilibrium of a rigid body
For an object to be perfectly still, it must not be moving in any direction, nor can it be rotating. This state of 'perfect balance' is called equilibrium, and it requires both forces and turning effects to cancel out completely.
Need to know
What you need to know
- **Translational Equilibrium:** The vector sum of all forces acting on the body must be zero. In 2D problems, this is usually broken down into two independent equations: $\sum F_x = 0$ (sum of horizontal components is zero) and $\sum F_y = 0$ (sum of vertical components is zero).
- **Rotational Equilibrium:** The sum of the moments of all forces about *any* point must be zero. This is often expressed as: Sum of Clockwise Moments = Sum of Anticlockwise Moments.
Explanation
The Perfect Balance
- Draw a large, clear diagram, marking all forces: weight (acting at the centre of mass), normal reactions, friction, and tensions.
- Resolve forces into two perpendicular components (usually horizontal and vertical). Set the sum in each direction to zero.
- Select a strategic pivot point. Set the sum of clockwise moments about this point equal to the sum of anticlockwise moments.
- Solve the system of equations generated from the force and moment conditions to find the required unknowns.