The Rolling Shutter Effect

Geometry Level 5

You might want to know what the Rolling Shutter Effect is about before attempting this question.

A Ball of radius 1/2 is spinning around a point (and always touching that point), which is at the center of the (blue) square, of side 2, as shown in the GIF above. The Black Line, or the Shutter, that moves from the bottom to the top of the screen, takes 2 seconds to travel across the square. The Blue Lines, which form a shape when the Shutter passes over it, is the image. At the start, the Black Line touches the bottom of the square while the Ball touches the top of the square.

Given that the fastest possible speed of the ball (In revolutions per second) such that the image shows a single, egged-shaped shape is \(A\), find

\[\left\lfloor 100000A \right\rfloor \]

(The first GIF from the top shows the image generated at speed \(A\))

This is the image generated at speed \(>A\)

This is the image generated at speed \(<A\)

A \(V\) shaped shape, which occurs in the case when 2 egged shaped shapes combine is not counted.


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