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Tether rotation device in space problem

  1. Jan 15, 2013 #1
    1. The problem statement, all variables and given/known data
    A spaceborne energy storage device consists of two equal masses connected by a tether and rotating about their center of mass. Additional energy is stored by reeling in the tether; no external forces are applied. Initially the device has kinetic energy E and rotates at angular velocity ω. Energy is added until the device rotates at angular velocity . What is the new kinetic energy of the device?

    (The answer is 2E but I don't see how)

    2. Relevant equations
    kinetic energy = 1/2*mv^2
    momentum = mv = mωr
    initial momentum = final momentum

    3. The attempt at a solution
    I don't see how this "energy storage" works. If I real the tether in, the radius r of the device decreases but the angular velocity ω of the device increases because of the conservation of momentum. The kinetic energy of the device is 1/2*m(ωr)^2, but the quantity ωr does not change. So I don't see how the potential energy of the device can be converted.
     
  2. jcsd
  3. Jan 15, 2013 #2

    gneill

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    Staff: Mentor

    ω and r both change when the device is reeled in. Call them ω1 and r1. The product of angular velocity and radius is what remains constant, so that ω1*r1 = ω*r.
     
  4. Jan 15, 2013 #3
    Right. If ω1*r1 = ω*r, then the kinetic energy stays the same. I still don't understand what the problem is talking about with the "stored energy," because reeling in the tether doesn't affect the energy.
     
  5. Jan 15, 2013 #4

    gneill

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    Staff: Mentor

    Ah. Sorry, I misspoke. Angular momentum is conserved, so it's Mωr2 that remains constant. Since M is the same in both cases, ωr2 is what you need to worry about. The square makes a difference :smile:
     
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