The Rattlebackthat Defies Convention

The rattleback is a top that defies convention. It spins freely in one direction, but if spun in the other direction, its rotational motion becomes

unstable; it starts to wobble and then will begin to spin in the opposite direction. In this regard, the rattleback seems to defy the physical law of

conservation of angular momentum.

The rattleback is shaped as an elongated asymmetric semi-ellipsoid with a flat top. The unintuitive reversal of the rotational motion occurs because of its

asymmetry. The asymmetry of the rattleback and frictional force from the table surface cause the rotational motion of the rattleback to become unstable.

The friction transfers energy from the spinning (rotational energy) to the wobble (vibrational energy). The vibrational energy is then transferred back to

rotational energy but in the preferred direction. Rotation in the preferred direction can also be initiated by pushing down on one end of the rattleback. This

vibration is then transferred to a rotational energy.

The rattleback provides an opportunity to demonstrate many physics concepts in the classroom.

What are the axes of rotation? The rattleback has three primary axes of rotation. It can spin about its center vertical axis.

It can roll about its horizontal long axis, and it can rock or wobble about its horizontal short axis. In boating terms, these are

called yaw, roll and pitch.

Have your students identify these axes and sketch the shape of the rattleback in each case. The asymmetry in

the shape can be seen when you look at the rattleback along the line of the long horizontal axis.

Why isn’t angular momentum conserved? Conservation of angular momentum is really just a special case of Newton’s

second law of rotation when there is no net external torque (force applied at some distance from a rotation axis). In the case of

the rattleback, however, there is a torque caused by the friction from the table top.

Try spinning the rattleback on various surfaces to illustrate the importance of friction.

What is Newton’s second law of rotation? dtLd

ext=∑τ [1]

Angular momentum ( L ) is only conserved when there is no net external torque (ext∑τ ). In the rattleback case, the torque

comes from the frictional force, which acts in a direction opposite to the direction of the spinning.

Angular momentum depends on the angular velocity (ω ) and the rotational inertia (I):

ωIL = [2] where ∑= ii dMrI 2

[3]

The rotational inertia is defined by the distribution of mass (M) at a distance r from the axis of rotation. In rotation, objects

behave differently based on the distribution of mass about the axis of rotation.

You can demonstrate this with a simpler example than the rattleback:

Take two PVC pipes of equal length. Add a high density material (like clay or steel washers)

to the middle section of one. Divide the same mass in half and add equal parts to the end

sections of the second pipe. The pipes will weigh the same, but the distribution of the mass

and, therefore, the rotational inertia will vary.

Have students quickly rotate the pipes back and forth (by gripping them at the middle) and

describe the differences in their movement. Which is harder to rotate?

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dM

dt

The rattleback is a great example of physics at work and the

complexities of describing what appears to be a simple toy.

Researchers have worked over decades to describe the motion

of the rattleback in both physical and mathematical terms.

Complicated mathematical equations and numerical models have

been developed to simulate this behavior. But physicists who

try to describe the physical behavior still struggle to intuitively

understand it! The world’s most pressing problems in science,

medicine, engineering and our natural environment are complex

in much the same way.

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How does stability come into play? Objects in rotation

preferentially spin around the axis with the smallest rotational inertia

(eqn. [3]). Try spinning a book-sized block of wood in the air to demonstrate

this. Spinning the wood around the longest or shortest axis of rotation is

stable and the wood continues to spin. However, it wobbles when spun

around the intermediate length axis.

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References:

Physics http://www.4physics.com:8080/phy_demo/rattleback.htm

Walker, J. The Flying Circus of Physics, 2nd ed., Wiley, 2007(www.flyingcircusofphysics.com)

Crane, H.R. “How things work: The rattleback revisited.”The Physics Teacher, 29(5):278-9, 1991.

Simulationshttp://www.tu-chemnitz.de/ifm/english/e_ifm_ala4bsp_rattle.htm

http://www.autolev.com/WebSite/SampleProblemRattleback/Rattleback.html

Historyhttp://128.174.130.156/LectDemo/descript/1148/more%20info.html

http://en.wikipedia.org/wiki/Rattleback

The rattleback is more complicated in its

instability due to the asymmetry around

the axis with the smallest rotational inertia.

However the instabilities are demonstrated

when you tap the end of the rattleback. In this

case, you are rotating the rattleback around

the intermediate axis (short horizontal axis),

which is the most unstable, similar to the

book example. The wobble (rotation about the

intermediate axis) is unstable and turns into

rotation about the axis that is most stable.

Largest inertia

Intermediate(unstable)

Longest axis has the smallest rotational inertia