The diameter of a long playing vinyl record is 12 inches. The unused center has a diameter of 4 inches, and there is a smooth outer edge that is 1 inch wide. If there are 91 grooves to the inch, how far does the needle travel within the groove during playback of the record?

I see two similarities between this problem and "Lotta Yotta" (pid 221)

First is the fact that in both cases an obsolete (or practically obsolete) recording medium is used.

The second, and more interesting, is that in both cases, we have an Archemedian spiral contained between two concentric circles, and we need to relate the length of the spiral to the area between the circles, given the separation between two consecutive "arms" of the spiral.

It is interesting that Charlie's first answer to this problem is similar in reasoning to my first answer to "Lotta Yotta."

 

Posted by TomM on 2005-04-02 00:40:09