Centrifugal acceleration - radians^2?

[EinsteinKillr]

Homework Statement

I'm working a problem concerning centrifugal acceleration and I've stumbled on something I don't quite understand:

Homework Equations

F=mrω² where ω=rad/s

So the resulting units: kg * m*rad²/s²

The Attempt at a Solution

I would expect acceleration to be in unit ms^-2


What's up with these radians? What do they mean?

 

[grzz]

Note that there is 'linear acceleration' (i.e. rate of change of linear volocity) in m/s^2
and 'angular acceleration' (i.e. rate of change of angular velocity) in mrad/s^2 but of course radian is not an S.I. unit.

 

[Doc Al]

The radian is a dimensionless quantity. It's a unit of angle (really a ratio) that has no dimension, so the final units of acceleration will be m/s² as expected. (See: http://en.wikipedia.org/wiki/Radian#Dimensional_analysis)

 

[grzz]

'radian' is a measure for an angle.
For example pi radians is equivalent to 180 degrees.

 

[EinsteinKillr]

The radian is a dimensionless quantity. It's a unit of angle (really a ratio) that has no dimension, so the final units of acceleration will be m/s² as expected. (See: http://en.wikipedia.org/wiki/Radian#Dimensional_analysis)

I've never consider that a radian is a ratio of a circle. Thanks! that makes a lot more sense.