Actually, as a record (or CD/DVD) spins in the drive and the needle (or eye) moves closer or further from the center, the angular velocity of the record (or CD/DVD) increases as it moves closer and decreases as it moves further.
Just to be pedantic, record players are CAV, while audio CDs, video DVDs, and video Blu-rays are CLV. Data optical discs can be either CAV or CLV.
So the needle of a record player will cover more ground at the start of each side (outside) than it will at the end (inside). The result was greater fidelity at the beginning of each side, because the needle was covering more linear space each second, and could pack more detail into each second.
This was well known to mastering engineers (and bands), and they would often take this into consideration when deciding what order to put the tracks on a record. Audio CDs eliminated this concern with CLV. Each "pit" took up the exact same linear distance, and each second had the exact same number of "pits". If you have an audio CD player with a window showing the disk as it spins, you can see the speed change when you skip tracks. This is especially visible when skipping from the last track to the first on a long CD.
Here is a neat image to help keep them straight.
On an AE FE map, the sun would have to be CAV for a day to be a consistent 24 hours.