calculations
Let's say record player rotation speed is 45 RPM, and camera frame rate is 30 fps.
When we convert minutes to seconds 45 RPM becomse 45/60 RPS, or 0.75 RPS.
The qestion is how many slices we need?
In 30 frames we can se 3/4 of whole record rotation.
Then, how many frames, images we need to draw on whole circle, to see all in one rotation?
In other words, it is direct proportion:
30 fps 0.75 rps
x frames? 1 round
x = 30 * 1 / 0.75 = 40 frames
Or use this simple calculator to find nice combinations:

