# Gyroscopic precession

1. Apr 12, 2004

### cucumber

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. Apr 12, 2004

$$\theta r = s$$
$$\omega r = v$$
$$\alpha r = a$$
$$\vec{L} = \vec{r} \times \vec{p}$$
$$\vec{\tau} = \vec{r} \times \vec{F}$$

3. Apr 13, 2004

### cucumber

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. Apr 13, 2004

### Chen

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: $$s = \theta r$$

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

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

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

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