If you drop a pebble down a mine-shaft, it will not fall vertically, but will be deflected slightly to the East by the Coriolis force, an effect of the Earth's rotation. We can solve the equations to calculate the amount of deflection; for a ten-second drop, the pebble falls about 500 metres (air resistance is … Continue reading Dropping Pebbles down a Mine-shaft
Month: October 2022
From Sub-atomic to Cosmic Strings
The two great pillars of modern physics are quantum mechanics and general relativity. These theories describe small-scale and large-scale phenomena, respectively. While quantum mechanics predicts the shape of a hydrogen atom, general relativity explains the properties of the visible universe on the largest scales. A longstanding goal of physics is to construct a new theory … Continue reading From Sub-atomic to Cosmic Strings
Finding the Area of a Field
It is a tricky matter to find the area of a field that has irregular or meandering boundaries. The standard method is to divide the field into triangular parts. If the boundaries are linear, this is simple. If they twist and turn, then a large number of triangles may be required. When we have the … Continue reading Finding the Area of a Field
CND Functions: Curves that are Continuous but Nowhere Differentiable
A function $latex {f(x)}&fg=000000$ that is differentiable at a point $latex {x}&fg=000000$ is continuous there, and if differentiable on an interval $latex {[a, b]}&fg=000000$, is continuous on that interval. However, the converse is not necessarily true: the continuity of a function at a point or on an interval does not guarantee that it is differentiable … Continue reading CND Functions: Curves that are Continuous but Nowhere Differentiable
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