## Friday, September 06, 2013

### The LP RPM Paradox

Th LP rpm paradox is one that  Patrick Hughes and George Brecht never tread upon
as Bill Watterson bravely once did:

The Calvin and Hobbs comic above deftly summarizes the situation. If any two points on a LP are rotating at the same speed, say 33rpm, how can they rotate different distances?  The distance around the outer edge is 37.68 inches, (12" diameter x pi) the last groove might only be six inches around ... How is this possible?

The fundamental confusion here is that speed is not the speed you are thinking of. It's a confusion between linear speed and angular speed. To be fair, the relation between linear speed and angular speed is less than intuitive.

In physics, angular frequency (aka angular speed) is a scalar measure of rotation rate. Every point on the record has the same angular frequency. Linear speed = the radius x angular speed. So the angular speed can be constant (33 rpm) while the linear speed is different at each point along the groove. So it's not that the common understanding of rotational speed is wrong, just that it's incomplete. More here.

In reality, linear speed still matters.  Hypothetical audio quality decreases over the length of the record because the distance around the inside of a 12-inch record is less than half the distance than around the perimeter. As the distance around each revolution decreases, the high frequencies become harder for a playback stylus to read. Most audio engineers will tell you flatly that those frequencies simply can't be reproduced on inner grooves as outer grooves. This is because the shorter rotations are equivalent to a reduced sample rate. Audiophiles often wont put more than 16 to 18 minutes per side. More here and here.