# Amazing Math Applications: Movement Inside a Sphere

## Modeling how a particle moves on the inside of a sphere

5 min readJan 15, 2024

I never fail to be amazed at how — in a few lines of formulae— a complex looking real life situation can be modelled with math. Consider the following problem:

*A particle of mass m rests at the bottom inside a hollow smooth sphere with center O. It is then projected along the inside surface until it reaches a point P in the upper hemisphere where it leaves the surface. It then moves through the hollow space inside the sphere*…