Centrifugal Force and Angular Velocity

  1. 1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations
    [tex]\vec{F_{cen}}=-m\omega\times(\omega \times r')[/tex]


    3. 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?
     
  2. jcsd
  3. 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.
     
  4. PhanthomJay

    PhanthomJay 6,269
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
  5. That makes better sense. Thank you!
     
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