M/deg^2 to m/rad^2 conversion

[Aerstz]

Homework Statement

Whitworth quick return mechanism. Rotational input in degrees results in linear slider acceleration (output) in meters. Convert this acceleration from meters per degree squared to meters per radian squared. (The angle substitutes time.)

Homework Equations

Multiplication factor (m/deg^2 to m/rad^2): 57.296^2

The Attempt at a Solution

See the above multiplication factor. Is that correct? If so, why is it squared and not simply 57.296, which is the conversion factor between radians and degrees?

 

[HallsofIvy]

Perhaps because you are talking about degrees squared and radians squared, not just degrees and radians? Doesn't that make sense to you? You are aware that there are 12 inches to a foot but 144 square inches to a square foot aren't you? There are 180 degrees to $\pi$ radians so $180^2= 32400$ degrees to $\pi^2$ radians.

That is, $"x m/deg^2= x m/deg^2*(32400 deg^2/\pi^2 rad^2)= (32400/\pi^2)x m/rad^2$

Of course $32400/\pi^2= (180/\pi)^2= (57.296)^2= 3283$ as you say.

 

[Aerstz]

Some days I can be completely blind to number logic. Today is one of those days. Thank you for your reply, I'm very grateful.