Level 7: Moving in circles

Forces and motion · level 7 of 8 · rough age 15-16 (a guide for parents; anyone can start anywhere)

In this level you work out the acceleration of anything moving in a circle, \(v^2/r\), and the force that has to supply it. Then you use it on Mars, where weak gravity means less grip: how fast a vehicle can take a bend, how a banked track helps, when a buggy leaves the ground over a bump, and how a spinning room could give people on Mars their full Earth weight back.

Lesson	You will be able to
Centripetal acceleration	Derive and use \(a = v^2/r = \omega^2 r\)
Centripetal force	Find the inward force needed, and name what supplies it
Cornering on flat ground	Find the top speed for a bend, and show it is 0.62 times Earth's on Mars
Banked tracks	Find the speed a banked curve is built for, with no friction needed
Loops and hills	Find the speed at which a vehicle leaves the ground over a crest
Spinning for gravity	Design a spinning room on Mars that gives full Earth weight

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