Confused by wikipedia on (torque-free) precession

In summary, the concept of torque-free precession explains how a plate thrown with some rotation around an axis that is not its axis of symmetry will have a constant angular momentum (L) in the absence of torques. This is due to the non-constant moment of inertia tensor (I) in the external reference frame. The spin angular velocity vector (ωs) about the spin axis must evolve in time so that the matrix product L = Iωs remains constant. This can be better understood by defining the angular momentum in either the stationary frame or the moving frame (fixed in the body and rotating with it). Using Euler's equations in the moving frame can help determine the equation for ω.
  • #1
nonequilibrium
1,439
2
Hello, I quote http://en.wikipedia.org/wiki/Precession from the first paragraph from the first section ("Torque-free precession"):

For example, when a plate is thrown, the plate may have some rotation around an axis that is not its axis of symmetry. This occurs because the angular momentum (L) is constant in absence of torques. Therefore it will have to be constant in the external reference frame, but the moment of inertia tensor (I) is non-constant in this frame because of the lack of symmetry. Therefore the spin angular velocity vector (ωs) about the spin axis will have to evolve in time so that the matrix product L = Iωs remains constant.

But isn't the matrix product L = Iωs relative to the moving frame (that's how we did it in our course anyway), meaning L and omega are indeed the vectors as defined/seen from the absolute/fixed frame, but the matrix product has the components from the moving/relative frame. In that case, those components of L don't have to be fixed, since a fixed L in the absolute frame will seem to be rotating/changing when seen from the moving frame.
 
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  • #2
hello mr. vodka! :smile:
mr. vodka said:
But isn't the matrix product L = Iωs relative to the moving frame (that's how we did it in our course anyway), meaning L and omega are indeed the vectors as defined/seen from the absolute/fixed frame, but the matrix product has the components from the moving/relative frame. In that case, those components of L don't have to be fixed, since a fixed L in the absolute frame will seem to be rotating/changing when seen from the moving frame.

the angular momentum (I) is best defined in the moving frame (the frame fixed in the body and rotating with it) because it's fixed in the structure, and in a stationary frame it would be changing

but you can define the angular momentum in the stationary frame, which is what wikipedia is doing to make it clear that a constant Iω and a changing I means a changing ω

we can work in either frame …

if all we want to show is that ω must be changing, then the stationary frame is easiest, but if we want to actually find the equation for ω, it's best to use the moving frame and Euler's equations :wink:
 
  • #3
Aha, that makes a lot of sense, thank you! :)
 

Related to Confused by wikipedia on (torque-free) precession

1. What is torque-free precession?

Torque-free precession is a type of rotational motion in which an object rotates around a fixed axis without any external forces causing it to do so. This means that the object's angular momentum is conserved, and there is no torque acting on it.

2. How is torque-free precession different from regular precession?

In regular precession, an object rotates around a fixed axis due to the influence of an external torque. In contrast, in torque-free precession, there is no external torque acting on the object, and its rotational motion is entirely due to the conservation of angular momentum.

3. What are some examples of torque-free precession?

One common example of torque-free precession is the rotation of a spinning top. As the top loses energy due to friction, it begins to precess around a fixed point without any external forces acting on it. Another example is the precession of the Earth's axis, which is caused by the gravitational pull of the Sun and Moon but appears to be torque-free due to the conservation of angular momentum.

4. What are the applications of torque-free precession?

Torque-free precession has various applications in physics and engineering. It is used in gyroscopes, which are devices that measure and maintain orientation. Torque-free precession is also used in satellite stabilization and navigation systems, as well as in the design of spinning objects such as tops and wheels.

5. How is torque-free precession related to angular momentum?

As stated earlier, torque-free precession occurs due to the conservation of angular momentum. This means that the object's angular momentum remains constant throughout its rotation, and any changes in direction are due to the redistribution of this momentum. In other words, the angular momentum of the object is always perpendicular to the axis of rotation, which is why it appears to precess around a fixed point.

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