Why a bus leans in a turn
A platform tilts slowly. The tall narrow bus tips first, the low one second, the wide one last. A bus in a turn behaves the same way.
Drag to orbit the scene, scroll to zoom. Press “Run”.
What the experiment shows
In a turn a bus behaves as if gravity had tilted sideways. It tips when the vertical through the centre of mass passes outside the wheels. The higher the centre of mass and the narrower the track, the sooner it happens.
How to run it
- Press “Run”: the platform begins to tilt slowly.
- Note the tilt angle at which each bus falls.
- Compare: which bus has the largest angle and why?
Questions to discuss
- Why do double-decker buses take turns more slowly?
- How could a driver make a load on the roof less dangerous?
The science
A body tips when the tilt angle φ reaches tan φ = (b/2)/h, where b is the width and h the height of the centre of mass. The tall bus has tan φ = 0.45/0.7, φ ≈ 33°, the low one 52° and the wide one (2.4 m) 60°. In a turn of radius R at speed v the sideways acceleration a = v²/R “tilts” the effective gravity by tan φ = a/g, so tipping starts at v² = g·R·(b/2h).
Try it at home
Put a tall narrow box and a low wide box on a book and tilt the book slowly. Which falls first?
What to change in the editor
- Make the “low” bus as tall as the first one.
- Halve the tilting speed of the platform.