1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why is the change in angle of precession equal to dL/L?

  1. Feb 19, 2015 #1
    If a rapidly rotating gyroscope attached to a perch is released in a horizontal position -- that is, so that the axis of the gyroscope is horizontal -- the gyroscope will precess around it's perch. Let L represent its angular momentum. Let dL represent a small change in that momentum. Let dA represent the corresponding change in the angle of L. According to all the references I've found, dA = dL/L. I don't understand this. Shouldn't dL/L be the change in the sine of the angle, not the angle? See attached diagram. Thanks.
     

    Attached Files:

  2. jcsd
  3. Feb 19, 2015 #2

    RUber

    User Avatar
    Homework Helper

    It looks like dL and dA are both measured in radial coordinates.
    dL = L * dA will give you the appropriate measure to arrive at the point L(t + dt) in the illustration. If you were to use the sine, you would be headed to a point more than |L| away from the center.
     
  4. Feb 19, 2015 #3
    Your mention of radial coordinates jogged my memory. The angle in radians is the arc length / radius. The radius in this case is L. Since the arc length approaches dL as the length of dL decreases, dL/L approaches dA. I think that's the reasoning that's being used. Thanks for your help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook