Illustrated Physics
physics, drawn
Concept

Centre of gravity — where it appears

The single point at which a body's whole weight may be taken to act without changing any moment. It coincides with the centre of mass whenever the gravitational field is uniform across the body, and separates from it for anything large enough to feel a gradient — which is what raises a tidal torque.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Also named here as metacentre — the same set of essays touches all of them, so they are one junction rather than several.

A heeled hull, and the couple it makes. A rectangular hull of beam 3 m heeled 18°, with the waterline solved so that it displaces the same volume it did upright. The centre of buoyancy has moved 0.244 m to the low side, and weight and buoyancy now act along two lines 0.059 m apart — a couple that turns the hull back upright.

Why a ship comes back upright

Whether a floating body rights itself or rolls over is not decided by its weight, its density or how deep it sits. It is decided by the shape of the slice the water cuts through it, and the number that settles it can be worked out before the vessel is built.

fluids · Buoyancy Which failure comes first. The dividing line between a block that slides and one that tips over, for a horizontal push applied at the top. Sliding needs a force of μ_s times the weight; tipping needs the push's moment about the leading bottom edge to beat the weight's, which is the weight times half the width. The weight appears in both and cancels, so the boundary is the curve aspect ratio = 1/2μ_s and nothing else: not the mass, not how hard the block is pushed, and not what it is made of except through μ. At μ_s = 0.5 the dividing shape is as tall as it is wide; at μ_s = 0.2 it is 2.5 times as tall. Of the 5 objects marked, 3 sit above the line and go over rather than sliding: a paperback, standing, a full filing cabinet, a pint glass.

Slide or topple

Push a wardrobe and it goes over; push a brick and it skids. Both are held by the same friction and both are pushed by the same hand, and which of the two failures arrives first has nothing to do with how hard the push is. The floor decides it, by shifting where it pushes back.

mechanics · Free-body

Named alongside it

The objects these essays reach for when they reach for this one.

EquilibriumMetacentreStabilityBuoyancyCentre of pressureCoefficient of frictionContact areaFree-body diagramMoment armNormal forceRighting momentSecond moment of area

All concepts