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A motorbike stuntman goes from town to town riding his bike in a large sphere 6m in diameter made from steel wire. The wire is so thick the ball remains rigid while he rides inside it. See a video here.

The motorbike and rider are about 2m tall together. We might model this as a particle in the centre, so when the bike & rider are in the sphere, this particle is 2m from the centre of the sphere.

The wheels of the bike are 40cm in diameter. What is the minimum angular speed the wheels must rotate if the bike is to be able to go upside down over the top?

Can you draw a graph of the reaction force that the sphere exerts on the bike over time if the bike maintains this speed?