Statics of Rigid Bodies

• Lamina under y = f(x): x̄ = ∫xy dx / ∫y dx, ȳ = ∫½y² dx / ∫y dx.
• Solid of revolution about the x-axis: x̄ = ∫πy²x dx / ∫πy² dx.
• Standard results: solid hemisphere 3r/8, solid cone h/4 from the base.
• A body topples when the vertical through G passes outside its base.

Curved shapes

Set up the integrals carefully with the correct limits.

Hanging, resting and toppling

Suspended bodies hang with G below the suspension point. A body on a slope topples (rather than slides) if the vertical through G falls outside the base before limiting friction is reached.