Equilibrium of a rigid body — common mistakes

Always start by drawing a large, clear force diagram. Label all forces (weight, reactions, friction, tension), known distances, and angles. A good diagram is not just for clarity; it's often the key to identifying the correct components and perpendicular distances, and can earn you method marks even if your final calculation is incorrect.

A particle is an object with mass whose dimensions are considered negligible. We only analyse the forces causing it to translate (move). A rigid body has dimensions (size and shape), so in addition to translation, we must consider rotation. This requires analysing the moments of forces.

In theory, no. If a body is in equilibrium, the net moment about any point is zero. However, in practice, your choice of pivot is a crucial problem-solving strategy. Choosing a point where unknown forces act will make those forces disappear from your moment equation, simplifying the algebra significantly.

If a rod is non-uniform, its centre of mass is not at its geometric centre. The problem will either give you the position of the centre of mass, or you will be required to find it as an unknown variable (e.g., 'the centre of mass is a distance $x$ from end A').

This is a more advanced scenario that combines two limiting conditions. It means that the frictional force has reached its maximum value ($F = \mu R$) AND the normal reaction at one of the supports has become zero. You would apply both of these conditions to your equilibrium equations to solve for the unknowns.