real information

--- On Mon, 9/29/08, dave wrote:
From: dave
Subject: pendulum
To:
Date: Monday, September 29, 2008, 10:47 AM

Hey:
physics questions:

how does a pendulum, or a gyroscope behave differently if it was at a
pole vs the equator?

when you try to turn a gyroscope, it tends to react by moving in an
angle that's like 90 degrees off the direction of push.. why is this?
is it dependent on the rotational speed or something? could you spin
a gyro at a speed where the push would
be at different angles? (i.e.
is it adjustable)

I'm trying to wrap my head around what it is that a gyro is stable
relative to.

I've seen those giant pendulum(s) in museums, and it makes sense to me
that it would work pretty obviously at a pole, but not so much how it
would work at the equator. also, do those pendulum(s) have to be
offset/adjusted on a solar orbit basis? (i.e. does the time of year
'tweak' the progression of the pendulum, so that you could actually
have a calendar pendulum?)

absolutely no reason for this, I'm just sitting at work in a meeting
pondering these kinds of things. -- trying to develop a space warp
drive in my head. I think I'm getting close...






A gyroscope would behave the same - mostly - there's a different coriolis and centrifugal force due to the earth's rotation but it's minimal (if you stand on the equator it feels the same as standing on the pole except it's warmer). With the pendulum if it's swing axis is constrained like in a clock then again it's almost exactly the same, but with the free swinging Foucault pendulum (like in science museums) it is different. I find it hard to visualize but if you get an orange and imagine swinging a pendulum over the pole and over the equator you sort of get the idea. The 'plane' the pendulum swings in is fixed (more on this later) while the orange rotates underneath it.

So...

What is this plane of swing remaining fixed relative to (lovely sentence). The old answer is 'the fixed stars.' In other words the 'long distance' distribution of matter. You're talking about the origin of inertia. It's how I got into cosmology. Mach's Principle.

As to variations over the year, yeah I think you could due to the tilt of the Earth's rotation axis relative to it's plane of motion.

Why do gyroscopes kick a funny way when pushed? It's all to do with conservation of angular momentum. If you've got an object moving north and you hit it from the west it'll veer east. This is cos it's 'linear momentum axis' and you give it some 'easterly' momentum so it goes off in that direction to conserve linear momentum (the thing that hit it will lose easterly linear momentum). That's sort of intuitive. The funny thing about angular momentum is that the angular momentum axis points at 90 degrees to the plane of spin. So if you have a CD that's spinning in its usual horizontal configuration its ang mtm axis is pointing straight up or down depending on which direction it is spinning. So when you hit a gyroscope you're basically giving it angular momentum (at least if you hit it in a line that isn't coincident with the ang mtm axis) and it moves in a 'funny' direction to conserve ang mtm.

Does that help?