Question

2. Consider a dise of radius R centered the origin in space and rotating about the z axis in some inertial reference frame O (a) What is the maximum angular velocityw of the disc allowed by Special Relativity? Recall angular velocity is 2π times the number of rotations per second. (b) Consider an observer O sitting at the edge of the disk, rotating with it i. Is O an inertial observer? ii. What does O measure the circumference of the disc to be? Remember, he is moving with the dise, so this circumference is the rest circumference. iii. What does O measure the diameter of the disc to be? What does he therefore calculate the ratio of the circumference to diameter to be? Is this strange? What does this tell you about spatial geometry in non-inertial reference frames in special relativity?
Throughout this homework assignment, you may use c to denote the speed of light in both your work and final answers without using its numerical value. (This is actually preferred unless the problem requires the numerical value of c.)
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