Rolling race
Race a solid sphere, solid cylinder and hoop.
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Which reaches the bottom first?
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How it works & assumptions
Rolling acceleration is g sinθ/(1+I/(mR²)). The inertia factors are 2/5 for a solid sphere, 1/2 for a cylinder and 1 for a hoop. Position=at²/2.
Start from rest; ideal rigid bodies rolling without slipping, with enough static friction to prevent slipping and no rolling losses. Equal outer radii; g=9.81 m/s².
References: University Physics Volume 1, section 11.1: Rolling Motion · Physics, Appendix A Reference Tables, Table A20
This is an ideal mathematical model, not a measurement or a forecast.