Tonight, like many other nights, I spent some time in my room listening to The xx. If you don't know who they are, you should definitely look them up. Anyway, I also bought the album on vinyl, which is the version I listen to in my room. Then tonight, when I realized that the record player was an excellent example of circular motion, I had to stop everything and blog about it at once.
Here is a video of the phonograph playing VCR by The xx from their self-titled album The xx (sorry about the audio quality, it was recorded with my phone):
The record rotates at a constant angular velocity of 33-and-1/3 revolutions per minute (rpm), or about 1.11π radians per second. The distance from the center of the record to the tip of the needle is about 10 inches, making the circumference, or distance traveled about 20π inches for every revolution. Here are my calculations for linear velocity:
(33.3 rev/min)(20π in/rev)(1min/60s) = about 11.1π inches per second
I realize that the needle constantly moves toward the center, so these calculations would only be accurate for an instant, but they provide a rough translation from angular speed to linear speed.
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