Force and free-body diagrams

A practical starting point for turning a physical component into a solvable force model.

ENGINEERING PRINCIPLE

A free-body diagram isolates the body, identifies external interactions and creates a consistent sign convention before equations are written.

ΣF = ma
FundamentalsVerifiedReviewed 2026-08-09

Variables and units

  • ΣF = resultant external force (N)
  • m = mass (kg)
  • a = acceleration (m/s²)

Worked example

A 1,500 kg trolley accelerating at 2.5 m/s² requires a 3,750 N net force before rolling resistance or gradients are added.

Calculation method

  1. Isolate one body at a time.
  2. Draw each applied force, support reaction and weight once.
  3. Choose axes, resolve components and apply the force balance.

Practical applications

  • Fixtures and mechanisms
  • Machine-frame reactions
  • Vehicle and material-handling motion

Review boundary and reference

  • A correct equation cannot rescue an incomplete free-body diagram.
  • Include inertia only when the selected reference frame requires it.

Formula and displayed units independently checked for the stated conditions. This is not a code-compliance design method.

Source: Classical Newtonian mechanics; SI unit relationships follow NIST Special Publication 811.

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