Question

Take a cardboard disc (radius ~ 8 cm) (Fig.). 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.

Answer 1

When the disc spins, the numbers on the outer edge appear blurred or may disappear, while the letters near the centre remain visible.

This happens because all points on the disc have the same angular speed, but their linear (tangential) speed depends on their distance from the centre.

Using the relation:

v = rω

where:

• v = linear speed
• r = distance from the centre
• ω = angular speed

Since the numbers are farther from the centre (7 cm) than the letters (4 cm), they have a greater linear speed. Therefore, the numbers move past our eyes more quickly, making them appear blurred or disappear, while the letters move more slowly and remain visible.