# How do we calculate linear speed to rotation?

I often need to figure out the linear velocity to the rotational velocity. If a roller is rotating at #frame/n and the roller has a diameter D, what is the resulting linear velocity?

• this might help as well en.wikipedia.org/wiki/Angular_velocity Jan 14 at 9:26
• In some cases, this rig might be easier to animate backwards.. with the box driving the rollers. But you've probably already decided on that. Jan 14 at 11:09

Your question is not very clear about what you mean by "is rotating at #frame/n" because this means technically an acceleration/deceleration. Also the meaning of n is not clearly stated so I will assume it's a constant number. I can give a general explanation:
If you don't want to include simulated friction or slip losses, you simply need the Peripheral Speed of one cylinder. It can be calculated by P_s = pi * D * RPM where:
• pi ~ 3.1416 [no unit]
• D is your diameter [meter]
• RPM "rounds per minute" [1/minute] (in case of Blender it might be more useful to give it as RPS "rounds per seconds") resp. [1/second]
pi and D are known, so you only have to derive RPS from Blender's driver expression #frame/n which has to be in [1/minute] resp. [1/second]. For that you probably have to calculate the duration of one frame. If you have 24 FPS (see your Output Properties) then one frame lasts 1.0 seconds / 24.0 ~= 0.042 seconds. If you clarify your question, I can give a more detailed answer.