If I just make a statement such as "it took 5 seconds to rotate 360 degrees", how would I go about getting an exact answer for how many radians per second that that object rotated?

360 degrees is exactly [math]2\pi[/math] radians, so we simply do:

 

[math]\frac{2\pi \mbox{ radians}}{5 \mbox{ seconds}} = \frac{2 \pi}{5}\, \mbox{rad/sec}[/math]

 

You can convert degrees to radians with Google, just by typing "360 degrees in radians." You can also use Google to find the decimal value of [imath]\frac{2\pi}{5}[/imath].

Just use the conversion factor, [math]\frac{2\pi \mbox{ radians}}{\mbox{ 360 degrees}} = 1[/math], which you can freely multiply or divide any number by as needed to cancel out the units.

Okey, so you will see, 1 radian is the amount of degrees the radius "takes" when its put in the circumference,

 

pi radians = 180º

 

therefore:

 

2pi radians = 360º

 

And then Cap'n Refsmmat is right, the result would be [math]\frac{2 \pi}{5}\, \mbox{rad/sec} [/math]

Edited December 6, 201015 yr by Blopa