Question: How does one know that $\frac{1}{s}$ refers to rad/s as opposed to some other dimensionless unit per second?
Hi everyone,
Today I was working through this related rates problem.
My question isn't about the calculation but about the units of the solution. The lecturer ends up with a final solution $\frac{d\theta}{dt}=\frac{9}{125}[\frac{1}{s}]$. The lecturer then goes on to state, "This value is going to be in radians per second. Let's convert it to degrees per second."
Why is it assumed that this unit $\frac{1}{s}$ is radians per second? I understand that radians are a common and natural unit of angular measure. But if degrees are also a dimensionless quantity, how is one supposed to realise that $\frac{d\theta}{dt}=\frac{9}{125}[\frac{1}{s}]$ refers to radians per second as opposed to degrees per second?
Thanks kindly,
1MTris-HCLpH8point6