Physics

posted by .

Two astronauts, each having a mass M are connected by a length of rope of length d have a negligible mass. They are isolated in space, orbiting their center of mass at an angular speed of ù0. By pulling on the rope, one of the astronauts shortens the total distance between them to 0.54d. Treat the astronauts as point particles (in terms of their moments of inertia).

a) What is the final angular speed of the astronauts as a fraction/multiple of ù0? (E.g. If you find that the final angular speed is half the initial angular speed enter 0.5.). Use angular momentum conservation.

b) What work does the astronaut do to shorten the rope as a multiple/fraction of the quantity Md^2ù0^2 (which has dimensions of energy)? (Hint: Calculate the change in rotational kinetic energy of the system instead, since you have no idea how the astronaut actually carried out the shortening.)

  • Physics -

    The problem is just too easy, with both of them having the same mass. So the center of rotation is at the midpoint, and radius of rotation is half length.

    Itotal=2Ieach= 2*mr^2
    after reducting the length, then
    I total=2m*(r-.27r)^2

    conservation of momentum
    initial=final
    2mr^2*wi=2mr^2(.73)^2 wf^2
    solve for wf

    I get wf=wi(.73) in my head. check that

    work? find the change of KE in the before and after rotational energies

  • Physics -

    It's actually wf=wi(1/.54^2)=wi(3.43)
    I can't seem to get the second part though.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics-rotational dynamics

    Two astronauts, each having a mass of 75.0 kg, are connected by a 10.0 m rope of negligible mass. THey are isolated in space,orbiting their center of mass at speeds of 5.00 m/s. calculate A)magnitude of the angular momentum of the …
  2. Physics (very long question)

    Two astronauts (Fig. P8.68), each having a mass of 84.0 kg, are connected by a 10.0 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway betwen them at a speed of 5.80 m/s. Treating the …
  3. physics

    Two astronauts, each having a mass of 89.0 kg, are connected by a 10.0 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.60 m/s. Treating the astronauts as …
  4. physics

    Two astronaut, as shown in the figure, each having a mass of 62.0 kg, are connected by a 12.00 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating …
  5. physics

    Two astronaut, as shown in the figure, each having a mass of 62.0 kg, are connected by a 12.00 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating …
  6. physics

    Two astronaut, as shown in the figure, each having a mass of 62.0 kg, are connected by a 12.00 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating …
  7. physcis

    Two astronaut, as shown in the figure, each having a mass of 62.0 kg, are connected by a 12.00 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating …
  8. physics HELPP!!!!!!!

    Two astronaut, as shown in the figure, each having a mass of 88.0 kg, are connected by a 10.00 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 6.00 m/s. By …
  9. physics

    Two astronauts, each having a mass of 78.5 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.50 m/s. Treating the astronauts as …
  10. Physics

    Two astronauts, each having a mass of 61.9 kg, are connected by a 14.7 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.57 m/s. Calculate the magnitude of the initial angular momentum …

More Similar Questions