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?

Consider only one side of the record.

Clearly the length of the groove is a function of groove width and the area of the resulting annulus of grooves. The area of the annulus being the difference between the 4 inch diameter center circle and the 10 inch diameter circle to the outside groove, or, 25pi - 4pi = 21pi. So, the length of the groove is ...

21pi times 91 = 1911pi or 6003.583561 inches

Posted by CeeAnne on 2005-03-31 19:26:45