# Angular Momentum Problems

1. Nov 19, 2008

### jcumby

I am having a lot of trouble understanding this! I'm not even sure how to begin these :(

First problem:
Two ice skaters, both of mass 60 kg, approach on parallel paths 1.4 m apart. Both are moving at 3.2 m/s with their arms outstretched. They join hands as they pass, still maintaining their 1.4 m separation, and begin rotating about one another. What is their angular speed?

I think that this has to do with moment of inertia and the distance from the axis of rotation, but I am confused.

Second problem:
Two disks, one above the other, are on a frictionless shaft. The lower disk, of mass 440 g and radius 3.4 cm is rotating at 180 rpm. The upper disk, of mass 270 g and radius 2.3 cm, is initially not rotating. It drops freely down the shaft onto the lower disk, and frictional forces act to bring the two disks to a common rotational speed. a.) what is that speed? b.) what fraction of the initial kinetic energy is lost to friction?

I think that I should be using energy considerations here, but I'm not sure how I should set this up.

Third problem:
Two small beads of mass m are free to slide on a frictionless rod of mass M and length l. Initially, the beads are held together at the rod center, and the rod is spinning freely with initial angular speed $$\omega$$0 about a vertical axis. The beads are released, and they slide to the ends of the rod and then off. Find the expressions for the angular speed of the rod a.) when the beads are halfway to the ends of the rod b.) when they're at the ends, and c.) after the beads are gone.

I believe that I should treat the beads as point masses, but I am confused about where to go from here.

2. Nov 20, 2008

### tiny-tim

Hi jcumby!

(have an omega: ω )

i] Don't bother about moment of inertia … you can treat them both as point masses.

Use conservation of angular momentum … the angular momentum before they touch is the same as the angular momentum when they're turning.

ii] Part a): You don't need energy, only conservation of angular momentum, = ∑ Iω.

Part b): Rotational KE = ∑ (1/2)Iω2.

iii] Yes, point masses again.

And use conservation of angular momentum again (the radial speed of the beads doesn't matter, since it doesn't contribute to angular momentum )