Gyroscopic precession

  • Thread starter cucumber
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  • #1
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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.
 

Answers and Replies

  • #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
 
  • #3
20
0
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.
 
  • #4
977
1
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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