Gyroscopic Precession (Relationship with ωspin and ωprecession)

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In summary: This means that the rate of precession is inversely proportional to the square of the radius of the wheel and directly proportional to the angular velocity of the wheel. This makes sense because a larger wheel or a faster spinning wheel would have a greater tendency to precess.
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ILoveZerg
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Homework Statement



I am trying to find the relationship between the rate of precession(ωprecession) and the angular velocity of the wheel(ωspin). Here is a video that explains the problem well:
http://www.youtube.com/watch?v=ty9QSiVC2g0

Homework Equations



$$L = r X P = Iω$$
$$\tau = r X F$$

The Attempt at a Solution



http://demoweb.physics.ucla.edu/node/29
http://scienceworld.wolfram.com/physics/GyroscopicPrecession.html

So, above are the answers to my question. However, they do not do a very good job of explaining what the equations mean. The equation for ωprecession from the first link is:
[itex]ω_{precession} = \stackrel{\tau}{I\omega_{spin}}[/itex]
[itex]ω_{precession} = \stackrel{Mgr}{L}[/itex]

I am trying to understand these and really do not know where to go from here. Is it really as simple as [itex]ω_{precession} = \stackrel{Mgr}{Mr_{2}^2\omega}[/itex]?

Edit: I was doing some more thinking and in the above equation where I replaced Iw with Mr^2w. The r2 on the bottom is the radius of the wheel while r is the radius of the horizontal "rod".
 
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  • #2
ILoveZerg said:
Is it really as simple as [itex]ω_{precession} = \frac{Mgr}{Mr_{2}^2\omega}[/itex]?

Edit: I was doing some more thinking and in the above equation where I replaced Iw with Mr^2w. The r2 on the bottom is the radius of the wheel while r is the radius of the horizontal "rod".

Yes, that looks right (after changing \stackrel to \frac).
 

1. What is gyroscopic precession?

Gyroscopic precession is the phenomenon where a spinning object experiences a change in orientation when a torque is applied to it. This change in orientation is perpendicular to both the direction of the torque and the axis of rotation.

2. How is ωspin related to gyroscopic precession?

The angular velocity of the spin, ωspin, is directly proportional to the rate of gyroscopic precession. This means that the faster an object is spinning, the faster it will precess when a torque is applied.

3. What is the relationship between ωprecession and ωspin?

The relationship between the two angular velocities, ωprecession and ωspin, is given by the equation ωprecession = (T/I)ωspin, where T is the torque applied and I is the moment of inertia of the spinning object. This means that the precession rate is directly proportional to the spin rate and inversely proportional to the moment of inertia.

4. How does gyroscopic precession affect the stability of an object?

Gyroscopic precession can provide stability to an object by resisting changes in its orientation. This is commonly seen in gyroscopes used in navigation systems or in bicycles where the spinning wheels help keep the bike upright and stable.

5. What are some real-life applications of gyroscopic precession?

Gyroscopic precession has several real-life applications, including navigation systems, gyrocompasses, gyroscopic stabilizers in ships and airplanes, gyroscopic sensors in smartphones for orientation detection, and gyroscopic tools used by surgeons to stabilize their movements during delicate procedures.

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