I am writing a paper on circular motion. A function given is $$T=Msω^2L$$
The units for $ω$ are $\text{rad}/s$. What are the units for $ω^2$? Are they $\text{rad}^2/s^2$ or $\text{rad}/s^2$? If they are the latter, why does $ω^2$ the units the same as those for angular acceleration?
[Math] If I square a value units of radians, is the result in units of radians squared or is it still radians
anglemathematical physicsphysics
Best Answer
Radians are dimensionless, since they are defined as the ratio of arclength to radius when you look at what an angle cuts out of a circle. That ratio is length/length. So if $\omega$ has units radians/second the dimensional analysis treats that as $1/s$. Then $\omega^2$ has units $1/s^2$.