1.16 Centre of Gravity & The Principle of Moments

• The centre of gravity (sometimes called the centre of mass) of an object is the point through which all the weight can be considered to act
• The position of the centre of gravity of uniform regular solid is at its centre
  • For example, for a person standing upright, their centre of gravity is roughly in the middle of the body behind the navel, and for a sphere, it is at the centre

• For symmetrical objects with uniform density, the centre of gravity is located at the point of symmetry

The centre of mass of a shape can be found by symmetry

Stability

• The position of the centre of gravity of an object affects its stability
• An object is stable when its centre of gravity lies above its base

The object on the right will topple, as its centre of gravity is no longer over its base

• The wider base an object has, the lower its centre of gravity and it is more stable
• The narrower base an object has, the higher its centre of gravity and the object is more likely to topple over if pushed

The most stable objects have wide bases and low centres of mass

• The principle of moments states:

For a system to be in equilibrium, the sum of clockwise moments about a point must be equal to the sum of the anticlockwise moments (about the same point)

Diagram showing the moments acting on a balanced beam

• In the above diagram:
  • Force F₂ is supplying a clockwise moment;
  • Forces F₁ and F₃ are supplying anticlockwise moments

• Hence: F₂ × d₂ = (F₁ × d₁) + (F₃ × d₃)