# Waves in rotational motion

If a chain is spun at high speed and let go will that spin on the ground without collapsing, why and how ?

If due to a small bump on the road the spinning chain develops a transverse wave what is the speed of that wave ?

Your chain is made of small parts. If you spin it, you give a momentum to each of these parts, which basically means they move.

Now if you release the chain, the small parts keep moving, and if the chunk in front of them in the direction of their motion slows down they will push it as well as pulling their other neighbour connected on the other side. This gives the chain an inner mechanic tension that forces it to take a oval shape if you release it vertically, as gravity still forces it downward (would be circular otherwise).

The energy stored in the chain will progressively dissipate through friction with the air and the soil, the chain slowing down and eventually falling on the floor.

If it reaches a bump it might temporarily change the chain shape, depending on its momentum when this happens. The motion will propagate and eventually equalize by diffusion along the chain.

There is no way to answer your question about speed without a lot of details regarding the chain, the initial spin and the entire scene. But essentially the speed of propagation of the perturbation is the speed of sound inside the material of the chain.

• Hmm, from the theory of the book i was solving, it says the wave speed must equal the speed of propagation. Any idea why ? – Mohit Jani May 12 at 8:32
• Because this is the only way for the wave to communicate its energy to its surroundings. – Exocytosis May 12 at 8:43
• I was thinking of applying tension(as surface tension in a soap bubble) and using sqrt(T/mass density) to get velocity. Will that be right ? – Mohit Jani May 12 at 8:45
• No idea, I build finite elements simulations, not approximations or analytical solutions. – Exocytosis May 12 at 8:56