question number 6.2 in page 279:(adsbygoogle = window.adsbygoogle || []).push({});

A drum of mass M_A and radius a rotates freely with initial angular velocity w_A(0). A second drum with mass M_B and radius b>a is mounted on the same axis and is at rest, although it is free to rotate.

A thin layer of sand with mass M_s is distributed on the inner surface of the amaller drum. At t=0, small perforations in the inner drum are opened. The sand starts to fly out at a constant rate [tex]\lambda[/tex] and sticks to the outer drum. find the subsequent angular velocities of the two drums w_A and w_B. ignore the transit time of the sand.

ok obviously, we have conserved angular momentum and conserved linear momentum (no external force).

i.e I_Aw_A+I_Bw_B=I_Aw_A(0)

and (M_A+M_s)v0=(M_A-[tex]\lambda[/tex]t)(w_A)a+(M_B+[tex]\lambda[/tex]t)(w_B)b

where v0=w_A(0)*a

but i dont get it from the final answer which is the answer clue:

if lambda*t=M_b and b=2a then w_B=w_A(0)/8.

am i missing something here?

btw, the moments of inertia here are of a uniform think hoop, right?

which MR^2.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Angular momentum question (from kleppner's book).

**Physics Forums | Science Articles, Homework Help, Discussion**