Question

What are some applications of using radian measure?

Answer 1

In physics you use radians to describe circular motion, in particular you use them to determine angular velocity, `omega`.
You may be familiar with the concept of linear velocity given by the ratio of displacement over time, as:
`v=(x_f-x_i)/t`
where `x_f` is the final position and `x_i` is the initial position (along a line).
Now, if you have a circular motion you use the final and initial ANGLES described during the motion to calculate velocity, as:
`omega=(theta_f-theta_i)/t`
Where `theta` is the angle in radians.
`omega` is angular velocity measured in rad/sec.

(Picture source: http://francesa.phy.cmich.edu/people/andy/physics110/book/chapters/chapter6.htm)

Have a look to other rotational quantities you'll find a lot of ...radians!