# Relativistic Rotating Disk

Classical Mechanics Level 4

A disk with radius $$R=1 \space m$$ is rotating with a large angular velocity of $$\omega =2.5\cdot { 10 }^{ 8 }\space s^{ -1 }$$. According to relativistic kinematics, what is the ratio of the disk's circumference to its radius, as observed in an inertial frame where the disk does not translate?

Bonus Thought: According to elementary geometry, the answer is $$2 \pi$$. Is it? If not, what's going on here?

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