A record turntable of radius R rotates at angular velocity

Chapter 12, Problem 11P

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QUESTION:

Problem 11P

A record turntable of radius R rotates at angular velocity ω (Fig. 12.15). The circumference is presumably Lorentz-contracted, but the radius (being perpendicular to the velocity) is not. What’s the ratio of the circumference to the diameter, in terms of ω and R? According to the rules of ordinary geometry, it has to be π. What’s going on here?9

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QUESTION:

Problem 11P

A record turntable of radius R rotates at angular velocity ω (Fig. 12.15). The circumference is presumably Lorentz-contracted, but the radius (being perpendicular to the velocity) is not. What’s the ratio of the circumference to the diameter, in terms of ω and R? According to the rules of ordinary geometry, it has to be π. What’s going on here?9

ANSWER:

Solution 11P

Step 1 of 5:

In this question, we need have turnable record table, the circumference is presumably Lorentz- contracted, however the radius is not

We need to find the ratio of the circumference to the diameter

We need to obtain the solution in terms of   and  

However as per rules of geometry the solution has to be

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