Moment of Inertia

Mechanics · 1765

Equation: I = Σ m_i r_i² = ∫ r² dm
Field: Mechanics
Symbols: I moment of inertia · m_i a bit of mass at distance r_i from the axis · the sum or integral over the whole body
Year: 1765

Significance

The rotational counterpart of mass: how hard a body is to spin up, set not just by how much mass it has but by how far from the axis it sits — hence the square. Euler defined it in 1765. A flywheel puts its mass at the rim for exactly this reason; a figure skater pulls arms in to spin faster; a hollow shaft is nearly as stiff in torsion as a solid one for a fraction of the weight.

Skills

Follow, Draw and Stun

Machines

Otto Four-Stroke Engine Diesel Engine Stirling Engine

Required By

Angular Momentum Tip Offset and Spin Slide to Roll

Referenced by

equation

Angular Momentum Slide to Roll Tip Offset and Spin

machine

Diesel Engine Otto Four-Stroke Engine Stirling Engine

skill

Follow, Draw and Stun

Open on the Equations shelf — the interactive card, the filters, and everything alongside it.

From the Equations database in Notion, last edited 2026-08-18. This page is the row, rendered by the build; nothing on it is written by hand.