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

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Elomis
Posts: 1
Joined: Mon Jan 14, 2008 10:09 am UTC

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

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?

Solt
Posts: 1912
Joined: Tue Mar 27, 2007 5:08 am UTC
Location: California

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

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.
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alterant
Posts: 32
Joined: Fri Feb 15, 2008 1:34 am UTC

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

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.

Charlie!
Posts: 2035
Joined: Sat Jan 12, 2008 8:20 pm UTC

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

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 Anyhow, I don't think anyone calls it "gyroscopic force," just torque.
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alterant
Posts: 32
Joined: Fri Feb 15, 2008 1:34 am UTC

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

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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