Describe, qualitatively, the effect of the position of the centre of gravity on the stability of simple objects

1.5.3 Centre of Gravity – Stability of Simple Objects

What is the Centre of Gravity?

The centre of gravity (CG) is the point at which the weight of an object can be considered to act.

If you balance a stick on your finger, the CG is the point where the stick will stay level.

Mathematically, for a uniform object the CG is at its geometric centre, but for irregular shapes it can be anywhere inside the body.

Why Does CG Matter for Stability?

Stability is the ability of an object to return to its original position after being disturbed.

The key factors are:

  1. Height of CG: Lower CG → more stable.

  2. Base of support: Wider base → more stable.

  3. Weight distribution: Concentrated near the base → more stable.

Analogy: Balancing a Pencil ⚖️

Imagine balancing a pencil on its tip.

If the CG is high above the tip, the pencil will tip over quickly.

If you lower the CG by bending the pencil slightly (making it thicker at the tip), it becomes easier to keep balanced.

This shows how lowering the CG improves stability.

Examples of CG and Stability

  • 🏀 Basketball vs. Volleyball: The basketball has a lower CG relative to its size, so it rolls less easily than the lighter volleyball.

  • 🛠️ Toolbox: A toolbox with a tall, narrow shape has a high CG and can tip over if not stored upright.

  • 🏗️ Skyscraper vs. Cottage: The tall building has a higher CG; engineers must design a wide base and strong foundations to keep it stable.

  • 🚶‍♂️ Human posture: Standing upright gives a lower CG than lying down, making a person less likely to fall.

Tipping Point – The Critical Angle

When an object is tilted, the line of action of its weight passes through the CG.

If this line falls outside the base of support, the object will tip.

The angle at which this happens is called the critical angle.

Mathematically, for a rectangular block of width \(w\) and CG height \(h\):

\$\tan(\theta_{\text{crit}}) = \frac{w/2}{h}\$

So, a larger \(w\) or smaller \(h\) increases \(\theta_{\text{crit}}\), meaning the object can be tilted more before tipping over.

Quick Reference Table

ObjectCG Height (relative)Stability
Tall flagpoleHighLow – easily tips in wind
Low garden shedLowHigh – very stable
Human standingModerateStable if feet spread wide

Key Takeaways

  • Lowering the CG always improves stability.

  • Increasing the width of the base of support also improves stability.

  • For any object, the critical angle can be calculated using the CG height and base width.

  • In engineering, designers use these principles to build safe bridges, towers, and everyday objects.

Remember: Think of the CG as the invisible “balance point” that decides whether an object will stay upright or tip over. By controlling its position, we can design objects that are safe, functional, and fun! 🎯