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.
The numbers fade or disappear because they are moving at a higher speed than the letters. This higher speed causes the numbers to blur together, making them fade or disappear to the human eye, while the slower letters remain visible.
The speeds of the numbers and letters are different. Justification: The distance travelled in one revolution is the circumference, 2πR. Since both take the same time T for one revolution, their speed is 2πR/T. The numbers are at a radius of 7 cm, while the letters are at 4 cm. Because the radius (R) is larger for the numbers, they cover a greater distance in the same time, resulting in a higher speed.
Explanation
The context provides the formula for average speed in circular motion: v_av = 2πR/T. Because the numbers are positioned at a greater radius (7 cm) compared to the letters (4 cm), they travel a larger circumference in the same time period T. Consequently, the numbers have a higher linear speed, causing them to blur and fade from sight, whereas the letters at a smaller radius move slower and remain visible.