Shape of Slinky being twirled in 0 gravity

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In summary, the shape of a Slinky being twirled in zero gravity showcases its unique ability to extend and coil without the influence of gravitational forces. As it spins, the Slinky maintains its structural integrity while the absence of gravity allows for a more fluid and dynamic motion, illustrating principles of physics related to tension and inertia.
  • #1
phantomvommand
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Homework Statement
Find the shape of a Slinky inside the International Space Station (i.e. in weightless conditions) if it is rotating uniformly – like a skipping rope – with both ends of the spring twirled in unison.
Relevant Equations
F = ma
I am able to understand the textbook solution, except for its very first assumption:
We use the coordinate system shown in the figure, and find the shape ofthe spring (assumed to have already attained its stable configuration) in this frame.

Screenshot 2024-05-29 at 5.29.36 PM.png

Why is it fair to assume that the slinky will ever reach a stable configuration (ie equilibrium)? Why can't it keep spinning around like a skipping rope?
 
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  • #2
phantomvommand said:
Why is it fair to assume that the slinky will ever reach a stable configuration (ie equilibrium)? Why can't it keep spinning around like a skipping rope?
A stable configuration just means its shape is not changing as it spins.
From the diagram, it appears the ends are anchored.
 
  • #3
haruspex said:
A stable configuration just means its shape is not changing as it spins.
From the diagram, it appears the ends are anchored.
Meaning to say, the x and y axes in the solution rotate, right? That clears it up. Thanks!
 
  • #4
phantomvommand said:
Meaning to say, the x and y axes in the solution rotate, right? That clears it up. Thanks!
That's not how I would put it. The coordinate axes can stay where they are; the spring rotates as though rigid about the x axis.
 
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If the motion is like a jump rope then the ##x## axis (the line between the anchored end points) would remain in place. One then has a choice to make.

One could use an inertial coordinates where points on the rope are rotating in the ##y## and ##z## directions. With this choice, the bits of rope would be subject to centripetal acceleration.

Or one could use rotating coordinates where the coordinate system rotates with the rope. Each point on the rope would have a fixed ##y## position while its ##z## coordinate would always be zero. With this coice, the bits of the rope would be stationary, but subject to centrifugal force.

My preference would be to use rotating coordinates and centrifugal force. One less coordinate to worry about. This appears to match the choice made by the people who posed the problem.
 

FAQ: Shape of Slinky being twirled in 0 gravity

1. What happens to a Slinky when it is twirled in zero gravity?

In zero gravity, a Slinky twirled in the air will not experience the same gravitational pull that it would on Earth. Instead, it will float and maintain its shape while the motion is governed by the force applied to it. The twisting motion will cause the coils to move outward and create a more elongated shape, as there is no weight pulling it downwards.

2. How does the lack of gravity affect the motion of the Slinky?

The absence of gravity means that the Slinky will not fall or compress under its own weight. As it is twirled, the centripetal force will dictate its movement, allowing it to expand and contract based on the applied force. The Slinky will behave more like a flexible spring, with its coils moving freely in response to the twirling motion.

3. Can a Slinky maintain its shape when twirled in zero gravity?

Yes, a Slinky can maintain its shape when twirled in zero gravity. The coils will remain intact and can stretch or compress based on the forces applied to it. However, without gravity, the Slinky will not settle into a typical resting position as it would on Earth, allowing it to continuously change shape while in motion.

4. What are the implications of twirling a Slinky in a microgravity environment?

Twirling a Slinky in a microgravity environment, such as on the International Space Station, can provide insights into the behavior of materials and forces in space. It can help scientists understand how flexible structures behave without the influence of gravity, which is important for designing equipment and materials for space missions.

5. How does the Slinky's behavior in zero gravity compare to its behavior on Earth?

On Earth, a Slinky experiences gravitational forces that influence its motion, causing it to fall and compress under its weight. In contrast, in zero gravity, it does not experience these forces, allowing it to behave more like a freely floating object. The lack of gravity enables the Slinky to display its elastic properties more prominently, resulting in different dynamics during twirling.

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