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Two body problemby Mathmos6
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#1
Mar2709, 05:48 AM

P: 82

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 2body 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
Mar2709, 08:25 AM

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P: 25,228

That sure seems correct to me. aI/mu doesn't even have the correct units, does it?



#3
Mar2709, 09:06 AM

P: 82

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? 


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