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We suggest an activity for measuring the speed of a bicycle going in circular motion by measuring the bicycle's lean angle. In this activity students will be able to feel the strength that is being activated on their bodies while they are moving in circular motion. They will also understand that it is impossible to ride in a circle without the bicycle leaning at an angle, an action that is performed intuitively.

In high-school teaching of mechanics, we deal, among other things, with the nature of static and kinetic friction, forces that are proportional to the normal force. Under the influence of frictional forces, a body moves down a rough sloped decline at a fixed rate of acceleration that is independent of its mass. This situation does not apply to cases where the frictional force is dependent upon velocity, such as bodies which are moving through a streaming fluid (such as raindrops falling to the ground). In this case the body moves with a continuously decreasing acceleration, eventually reaching a terminal velocity when the frictional and gravitational forces balance out. This velocity constraint is determined by the dependence of the frictional force on velocity and geometric parameters that determine the strength of the frictional force. We show here that a similar situation takes place when bicycles descend an incline with a fixed slope. We also investigated the dependence of the velocity constraint with mass, using bicycles equipped with sophisticated sensors that metamorphose them into data-processing laboratories.

For developing riding skills on mountain bikes, it is important to know how the centre of mass of a bicycle and its rider changes with ground inclination or with rider position. We show here a new method for finding the location of this point by measuring the normal forces acting on the wheels in two positions with a digital weight indicator. This method can be easily applied in the classroom and can be used as a real-life example for computing the centre of mass of a complex body. (Contains 1 table and 5 figures.)

So‐called fairy circles (FCs) comprise a spatially periodic gap pattern in arid grasslands of Namibia and north‐west Western Australia. This pattern has been explained with scale‐dependent ecohydrological feedbacks and the reaction‐diffusion, or Turing mechanism, used in process‐based models that are rooted in physics and pattern‐formation theory. However, a detailed ecological test of the validity of the modelled processes is still lacking.Here, we test in a spinifex‐grassland ecosystem of Western Australia the presence of spatial feedbacks at multiple scales. Drone‐based multispectral analysis and spatially explicit statistics were used to test if grass vitality within five 1‐ha plots depends on the pattern of FCs that are thought to be a critical extra source of water for the surrounding matrix vegetation. We then examined if high‐ and low‐vitality grasses show scale‐dependent feedbacks being indicative of facilitation or competition. Additionally, we assessed facilitation of grass plants for different successional stages after fire at fine scales in 1‐m2 quadrats. Finally, we placed soil moisture sensors under bare soil inside the FC gap and under plants at increasing distances from the FC to test if there is evidence for the 'infiltration feedback' as used in theoretical modelling.We found that high‐vitality grasses were systematically more strongly associated with FCs than low‐vitality grasses. High‐vitality grasses also had highly aggregated patterns at short scales being evidence of positive feedbacks while negative feedbacks occurred at larger scales. Within 1‐m2 quadrats, grass cover and mutual facilitation of plants was greater near the FC edge than further away in the matrix. Soil moisture after rainfall was lowest inside the FC with its weathered surface crust but highest under grass at the gap edge, and then declined towards the matrix, which confirms the infiltration feedback.Synthesis. The study shows that FCs are a critical extra source of water for the dryland vegetation, as predicted by theoretical modelling. The grasses act as 'ecosystem engineers' that modify their hostile, abiotic environment, leading to vegetation self‐organization. Overall, our ecological findings highlight the validity of the scale‐dependent feedbacks that are central to explain this emergent grassland pattern via the reaction‐diffusion or Turing‐instability mechanism. [ABSTRACT FROM AUTHOR]

Understanding advanced physical phenomena such as vertically hanging elastic column, soap bubbles, crystals and cracks demands expressing and manipulating a system's potential energy under equilibrium conditions. However, students at schools and universities are usually required to consider the forces acting on a system under equilibrium conditions, rather than taking into account its potential energy. As a result, they find it difficult to express the system's potential energy and use it for calculations when they do need to do so. The principle of least potential energy is a powerful idea for solving static equilibrium physics problems in various fields such as hydrostatics, mechanics, and electrostatics. In the current essay, the authors describe this principle and provide examples where students can apply it. For each problem, the authors provide both the force consideration solution approach and the energy consideration solution approach. [ABSTRACT FROM AUTHOR]