Statics

Conditions for static equilibrium and rest in translational and rotational mechanical structures.

General idea of the topic

Statics studies bodies in equilibrium: those whose linear and angular accelerations are zero. For an extended body to be in equilibrium it is not enough that the sum of forces is zero; the sum of moments about any point must also vanish.

The block separates three questions: translational equilibrium, which depends on the sum of forces; rotational equilibrium, which depends on the moments and on where the forces are applied; and the centre of mass, the point at which the mass of the body can be considered concentrated.

What the student is expected to understand

By the end, the student should be able to set up the equilibrium conditions of a rigid body, choose the axis that simplifies the moments and compute reactions and unknown forces.

The student should also be able to locate the centre of mass of a discrete system or of a continuous body.

Recommended learning route

1. Translational Equilibrium: zero sum of forces, free-body diagram and examples with supports, cables and planes.
2. Rotational Equilibrium: moment of a force, zero-net-moment condition and levers.
3. Centre of Mass: definition of the centre of mass and its calculation in discrete systems and in extended bodies.

Essential physical criterion

The essential criterion is to use both conditions at the same time and to choose the point for the moments wisely: if it is taken where an unknown force acts, that force disappears from the equation. A body can have zero net force and still rotate, and can have zero net moment and still translate.

Connection with real problems

• bridges, beams and structures.
• cranes, scales and levers.
• stability of vehicles and resting objects.
• biomechanics of the human body.

Final goal of the topic

The final goal is to analyse any body in equilibrium using the two conditions, compute unknown forces and locate the centre of mass.