1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Two body problem

  1. Mar 27, 2009 #1
    1. The problem statement, all variables and given/known data
    Two gravitating particles with masses m1 and m2 start from rest a large distance apart. They are allowed to fall freely towards one another. The particles are given equal and opposite impulses I when they are a distance a apart, such that each impulse is perpendicular to the direction of motion.

    Show that the total angular momentum of the two particles about their centre of mass has magnitude aI /µ, where µ is the reduced mass of the system.

    2. Relevant equations

    Reduced mass=m1m2/(m1+m2)

    3. The attempt at a solution
    Well this is the second last part of quite a long question on the 2-body problem, and I've managed fine until now (showing the position of the centre of mass 'C' - is constant, finding their relative speed etc) but I'm not sure how to go about this part of the question. The two particles are going to be moving in a straight line towards each other before the impulses which should mean 0 angular momentum before, so then the only angular momentum afterwards would be that from the impulses right?

    But the impulses are perpendicular to the direction of motion so with the r x p cross product we'd just have angular momentum=dist. from C * impulse in each case wouldn't we? The m2 mass particle should have a distance (m1/(m1+m2))a from C and the m1 particle a distance of (m2/(m1+m2))a, but then clearly I've done something wrong because the sum of the impulses will just be (m1+m2/m1+m2)aI=aI.

    Where am I going wrong? Thanks!
  2. jcsd
  3. Mar 27, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    That sure seems correct to me. aI/mu doesn't even have the correct units, does it?
  4. Mar 27, 2009 #3
    Actually that's a fair point, whereas aI does - weird! I'll check with someone else to see if the question is mistyped, but it seems odd that the entire "/µ, where µ is the reduced mass of the system." would be a mistake...

    I'll let you know if i find out! Do you think just aI is the correct answer then?
    Last edited: Mar 27, 2009
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Two body problem
  1. Two integral problems? (Replies: 4)