Tipping Point
Geometry & Trigonometry
These table tennis tables cannot be stored on slopes greater than 10 degrees.
Introduction
A folded table tennis table tips over once its centre of mass moves past its pivot edge — the same geometry that limits how steep a ramp, a stack of boxes, or a leaning ladder can be before it falls. The tipping condition reduces to right-angled trigonometry: tan(angle) compares the height of the centre of mass to its horizontal distance from the pivot edge, the point where the object touches the ground. Moments and torque are useful for explaining why this works physically, but they are not themselves examined in the IB AI or AA syllabus; the maths credited here is the trigonometry used to find the tipping angle.
Guiding Questions
- Where is the centre of mass of a table tennis table folded for storage, and how would you estimate it?
- Why does a slope make tipping more likely? Draw the forces and find the tipping condition.
- Can you show mathematically why 10 degrees might be the stated limit?
- How would the safe angle change if the table were taller, heavier at the top, or had wider feet?