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Homework Help: Gyroscopic precession

  1. Apr 12, 2004 #1
    hi. not sure if this belongs in here, so sorry in advance for any trouble caused.
    i am in a bit of a predicament with a physics assessment of mine; i need to know the mathematical relationships between the precessional frequency, the couple (or torque, as i have read it called) and the angular momentum of a gyroscope, and (here comes the tricky bit) i would like to understand it...
    i just need someone to point me in the right direction, i mean i hardly know which questions to ask or where to start looking (sob sob).
    i am quasi-familiar with the concept of moment of inertia being the equivalent of mass in linear motion and angular velocity that of velocity (duh), but i have not found a set of formulae that would allow me to make a connection between the aforementioned...er... things...

    i come with the rather unsound basis of a-level physics, which is why it will be an especially challenging task for you get me to understand it. good luck (and thanks).

    cucumber.
     
  2. jcsd
  3. Apr 12, 2004 #2
    [tex]\theta r = s[/tex]
    [tex]\omega r = v[/tex]
    [tex]\alpha r = a[/tex]
    [tex]\vec{L} = \vec{r} \times \vec{p}[/tex]
    [tex]\vec{\tau} = \vec{r} \times \vec{F}[/tex]

    cookiemonster
     
  4. Apr 13, 2004 #3
    thanks cookiemonster.
    i'm unsure about a couple of things, though...

    what are the "s" and the theta in [theta]*r = s

    what are the alpha and the "a" in [alpha]*r = a

    what are the "r"'s in both the above equations (just to be sure...)

    and finally, what are those two other equations all about???
    i suppose that funny looking thing (like half a pi) is torque, but the rest i have absolutely no idea... sorry.
    i'd be very grateful if you could clarify them a bit.

    thanks again.
    cucumber.
     
  5. Apr 13, 2004 #4
    In a circle of radius r the length of any arc is given by the angle it creates with the center of the circle times the radius: [tex]s = \theta r[/tex]

    Angular acceleration:
    [tex]\alpha = \frac{a_t}{r}[/tex]
    http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html#rq

    Angular momentum:
    [tex]\vec{L} = \vec{r} \times \vec{p}[/tex]
    http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html

    Torque ('tau'):
    [tex]\vec{\tau} = \vec{r} \times \vec{F}[/tex]
    http://hyperphysics.phy-astr.gsu.edu/hbase/torq2.html#tc

    Precession of Gyroscope:
    http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html#gyr
     
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