Centrifugal Force and Angular Velocity

[lylos]

Homework Statement

I'm working on a problem in which I have to calculate the centrifugal force. I know the equation and everything, I'm just stuck on what units my angular velocity should have.

Homework Equations

$$\vec{F_{cen}}=-m\omega\times(\omega \times r')$$

The Attempt at a Solution

I've evaluated the above with angular velocity having units rotations*s^-1. I know that angular velocity should have units rad/s but I'm wondering how one gets units of Newtons when using rad/s as the unit of angular velocity. I've never really understood this, what is so special about radians that you can ignore them when converting units?

 

[cashmoney805]

I'm not sure if I can fully answer your question, but I can at least answer some.

Why can you drop the degrees when you do cos(degree)? I don't know the answer, all I know is you just can.

You can get N from angular velocity this way. F = ma. In this case, a is centripetal acceleration, which is = w^2 * r. Now you get m/s^2, multiply that by mass and you get Newtons.

 

[PhanthomJay]

I've never really understood this, what is so special about radians that you can ignore them when converting units?

You don't just ignore them; a radian is a dimensionless unit of measure . A radian is defined as the arc length of a circle subtended by the central angle between 2 radii of a circle, divided by the radius of the circle, that is, rad=s/r, where s is the arc length subtended by the cenrtral angle, and r is the radius of the circle. As you should see, the radian has units of length/length, which is dimensionless. That's how you end up with Newtons as the centripetal force unit, as Cashmoney has noted.

 

[lylos]

That makes better sense. Thank you!