Local “reversal of gravity” can be simulated with an inverted pendulum whose pivot is made to oscillate vertically. A beautiful demonstration of this surprising effect can be found in Ref. 1. In this case, the pendulum is a piece of plastic straw and its pivot pin is fixed at the end of a plastic ruler that is made to oscillate vertically by a small eccentric motor. A theoretical treatment of this inverted pendulum may be found in Ref. 2.

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We propose a simple approach to determine all possible wheels that can roll smoothly without slipping on a periodic roadbed, while maintaining the center of mass at a fixed height. We also address the inverse problem that of obtaining the roadbed profile compatible with a specific wheel and all other related “quantized wheels.” The role of symmetry is highlighted, which might preclude the center of mass from remaining at a fixed height. A straightforward consequence of such geometric quantization is that the gravitational potential energy and the moment of inertia are discrete, suggesting a parallelism between macroscopic wheels and nano-systems, such as carbon nanotubes.

It is highlighted the vital importance of exposing engineering students to practical challenges at an earlier stage of their academic life in terms of motivation, thus contributing to decrease drop-outs, besides enhancing self-reliance and fostering creativity. We discuss different strategies adopted by teams of students to find out a problem and to translate it in terms of a feasible solution. Future developments and unfolding challenges are also addressed to provide a big picture of the complexities involved in fostering innovative thinking in academia.

Some years ago I visited the Cavendish Laboratory in Cambridge and was astonished by the simplicity of the devices that Maxwell and Thomson had used to make their fundamental discoveries. Back in Brazil, I decided to start a project to present physics to laypeople through demonstrations using simple materials that had been thrown away as refuse. I also encouraged the undergraduates on my introductory university physics courses – the maths, physics and chemistry teachers of the future – to produce simple demonstrations to explain the physics of everyday life.