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Take a cardboard disc (radius ~ 8 cm). Write numbers 1 to 12 on the outer part (7 cm from the centre) and the letters ‘ABCDEF’ on the inner part (4 cm from the centre), using the same font size. Spin the disc slowly, then faster, and observe how the numbers and letters appear. Why do the numbers fade or disappear while the letters remain visible? Are the speeds of the numbers and letters the same or different? Justify your answer.
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The outer numbers (7 cm out) move faster than the inner letters (4 cm in), because in one turn the outer marks cover a larger circle (\(2\pi R\) is bigger for larger \(R\)). The faster outer numbers blur and fade sooner as you speed up, while the slower inner letters stay readable longer. So their speeds are different even though they complete a turn in the same time.
