1. ## Unchained

A person is swinging a length of chain about them in a circular path, at 27 complete rotations per minute. The far end of the chain sweeps out a circle of 1 metre radius. A 20cm length of the chain breaks off at the far end. Ignoring gravity and air resistance, describe the motion of the detached fragment of chain.

Alan

2. ## Re: Unchained

As i am more practical than mathematical, i will describe it as: The 20cm piece flies off the end at 100 miles per hour, and crashes into the cars window that was standing in the vacinity! The chain then falls downwards scrapping the paint off the side of the door and lands on the roadside unharmed. The "swinger" runs away in fear of being arrested for vandalism!
Just my <img src=/S/2cents.gif border=0 alt=2cents width=15 height=15> <img src=/S/wink.gif border=0 alt=wink width=15 height=15> <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

3. ## Re: Unchained

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The midpoint of the segment will move in a straight line, tangential to the circle at the point where it broke off, with a speed of 2*pi*0.9*27 metres per minute, or about 2.54 m/s. The segment will rotate around the midpoint, 27 times/minute.</span hide>

4. ## Re: Unchained

<img src=/S/dizzy.gif border=0 alt=dizzy width=15 height=15>

And here was I just going to say it flies off in a straight line until it hits something!

<img src=/S/hailpraise.gif border=0 alt=hailpraise width=27 height=22> Hans!

5. ## Re: Unchained

<P ID="edit" class=small>(Edited by AlanMiller on 08-Jun-05 10:22. )</P>Well done Hans.

Edited - It's actually an interesting problem. I'm wondering what steps you used to work it out. I was hoping to use it as an example of the conservation of momentum - not just linear, but angular as well. I solved it without directly resorting to those principles, but I'm looking for a problem where you do need to use them.

Alan

6. ## Re: Unchained

I solved it intuitively, I guess using conservation of momentum as basic idea.

7. ## Re: Unchained

Attached is a crude visual representation of what Hans eloquently verbalized...

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