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## Main Question or Discussion Point

This problem came up after drawing a line on the spinning rotor of a food processor. I was idly musing about relativity (parallel motion and perpendicular motion). Maybe some ancient mathematician found the solution while working clay on their potting wheel! Here it is:

A flat disk rotates about (0, 0) on the (x, y) coordinate system. A point on the edge of the disk has angular velocity ω. During this rotation, a straight pencil line is drawn from the centre (0,0) along the y-axis toward the edge at linear velocity, v

Let the radius=1,

ω=1 rad^-2

v =1^-1

[Essentially, you draw the straight pencil line at the same velocity that each point on the disk's edge rotates.]

The disk stops rotating when the pencil line reaches the disk’s edge. Interestingly, the pencil line is revealed as curled, not straight.

Obviously when the line is uncurled it is longer than 1. Then what is the method to find out by how much?

A flat disk rotates about (0, 0) on the (x, y) coordinate system. A point on the edge of the disk has angular velocity ω. During this rotation, a straight pencil line is drawn from the centre (0,0) along the y-axis toward the edge at linear velocity, v

Let the radius=1,

ω=1 rad^-2

v =1^-1

[Essentially, you draw the straight pencil line at the same velocity that each point on the disk's edge rotates.]

The disk stops rotating when the pencil line reaches the disk’s edge. Interestingly, the pencil line is revealed as curled, not straight.

Obviously when the line is uncurled it is longer than 1. Then what is the method to find out by how much?