How do I calculate gyroscopic force? assuming it's name.. :(

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Elomis
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How do I calculate gyroscopic force? assuming it's name.. :(

Postby Elomis » Sun Mar 16, 2008 10:34 am UTC

Hey guys,

If I have a wheel which is 10kg in weight, and 1m in diameter and it spins at 10,000rpm, it will be very hard to move in a direction that isn't parallel to a line drawn from the middle to one edge, or from the middle outwards, perpendicular to the face of the wheel.

What I want to know is, I've been told this is 'gyroscopic force'. Is that true? if so, how do I calculate it? If not, what's it actually called and how do I calculate it? How MUCH harder is it to move the wheel than it otherwise would've been if the wheel was stationary?

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Solt
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Re: How do I calculate gyroscopic force? assuming it's name.. :(

Postby Solt » Sun Mar 16, 2008 1:07 pm UTC

The term you are looking for is "Angular Momentum." It is a vector quantity that acts perpendicular to the plane of rotation (the axis) according to the right hand rule.

I'd help more, but I'm sleepy.
"Welding was faster, cheaper and, in theory,
produced a more reliable product. But sailors do
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alterant
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Joined: Fri Feb 15, 2008 1:34 am UTC

Re: How do I calculate gyroscopic force? assuming it's name.. :(

Postby alterant » Sun Mar 16, 2008 5:13 pm UTC

It is indeed angular momentum, usually denoted L and given by:

L = Iω

where I is the moment of intertia of the object and ω is the angular frequency.
Moment of inertia has to be calculated from the geometry of the spinning object. For a thin disc spinning about its central axis, I = mr2/2 , so if it's 10 kg and 0.5 m in radius, we have I = 1.25 kg m2 .
The angular frequency can be calculated from the RPMs by:
--> Converting RPM to Rev/s (divide by 60), which gives you frequency;
--> multiplying frequency by 2π, which gives you angular frequency.
So ω = 10 000 min-1 * (1 min)/(60 s) * 2π = 1047.2 s-1

So L = 1309 kg m2 s-1

Sorry if you already knew some of this stuff.

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Charlie!
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Re: How do I calculate gyroscopic force? assuming it's name.. :(

Postby Charlie! » Sun Mar 16, 2008 5:59 pm UTC

I think he's looking for the opposing force you get when you try to tilt a gyroscope.

Fear not, for wikipedia knows! ( http://en.wikipedia.org/wiki/Gyroscope )
The fundamental equation describing the behavior of the gyroscope is:

Torque = dL / dt = d(I*w) / dt = I * angular acceleration

Where L is angular momentum, w in angular frequency and I is moment of inertia.

It follows from this that a torque applied perpendicular to the axis of rotation, and therefore perpendicular to L, results in a motion perpendicular to both T and L. This motion is called precession. The angular velocity of precession is given by the cross product:

Torque of precession = velocity of precession x L

pretend those were vectors :-D

Anyhow, I don't think anyone calls it "gyroscopic force," just torque.
Some people tell me I laugh too much. To them I say, "ha ha ha!"

alterant
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Joined: Fri Feb 15, 2008 1:34 am UTC

Re: How do I calculate gyroscopic force? assuming it's name.. :(

Postby alterant » Mon Mar 17, 2008 2:20 am UTC

Ah yes, you're right. The tricky bit in that equation is the angular acceleration, but I believe it can be calculated from the angular velocity at the edge of the disc:
α = -ω2r


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