# Stability of a Roly-poly

*Most recent answer: 04/29/2014*

Q:

I would like to know how I could calculate the relationship between mass, length, angle and diameter of base and amplitude of pivotal displacement of an object that is essentially vertical but with a low centre of gravity (such as a roly-poly toy) in order to predict its ability to self-right. Thank you!

- Caio Armbrust (age 25)

Brazil

- Caio Armbrust (age 25)

Brazil

A:

Hello Caio,

You have the right start when you mention "low centre of gravity". You have to calculate that point as well as the point at which the object rotates. If the center of gravity is below the center of rotation then it will be stable. If above, it will fall over. If the two points coincide, for example in a homogeneous sphere, then the object will be in a state of neutral equilibrium at any angle.

LeeH

*(published on 04/29/2014)*