Centre of Mass and Centre of Gravity

If you balance a ruler on your finger, there is one special point where it stays level. That point is its centre of mass (and, near Earth, also its centre of gravity).

Key ideas

Centre of mass is the point where an object’s mass is thought to be concentrated. Centre of gravity (CG) is the point where the object’s weight acts. Near Earth, these are effectively the same point.

• Weight acts as a single force through the CG: $W = mg$.
• When an object hangs freely, its CG lies directly below the support (along a vertical line).
• For uniform, symmetrical shapes, the CG is at the geometric centre. Holes or thicker parts move the CG toward the heavier side.

Finding the CG of an irregular lamina (card shape)

1. Make a small hole near the edge. Hang the lamina from a pin and hang a plumbline next to it. When still, draw a line down along the plumbline.
2. Repeat from a different hole and draw the second line.
3. The lines cross at the CG. This point balances the lamina.

Why this works: when hanging, the weight acts vertically through the pivot, so each line shows a vertical through the CG. The crossing point is the only place common to both verticals.

Stability and the CG

An object is stable if the line of action of its weight (a vertical through the CG) falls inside its base of support. If it passes outside the base, the object topples.

• Lower CG and wider base = more stable.
• Examples: racing cars have low CG; buses are designed to keep CG low; standing with feet apart widens your base; a tightrope walker uses a long pole to lower and spread mass.

Common misconceptions

• “The CG is always inside the object.” Not always—ring-shaped objects have a CG in empty space.
• “The CG is always at the shape’s centre.” Only if the material is evenly spread.
• Mass and weight are the same. Mass is the amount of matter; weight is the gravitational force $W=mg$ acting at the CG.