- #1
Cpt. DeMorgan
- 4
- 0
Homework Statement
In the figure a spherical non spinning asteroid of mass M = 4E16 kg and radius R = 1.5E4 m moving with speed v1 = 2.4E4 m/s to the right collides with a similar non spinning asteroid moving with speed v2 = 5.9E4 m/s to the left, and they stick together. The impact parameter is d = 1.4E4 m. Note that I_sphere = 2/5*M*R^2.
After the collision, what is the velocity of the center of mass and the angular velocity about the center of mass? (Note that each asteroid rotates about its own center with this same angular velocity. Assume that the asteroids move in the x-y plane, and that the asteroid of speed v1 moves in the positive x direction.)
Homework Equations
L_A,f = L_A,i
L_Rot = Iω, L_Rot = r1cm x p1 + r2cm x p2
L_tran = r_a,cm x p_tot
The Attempt at a Solution
I have found v_cm. Now I am looking for the angular velocity. I have considered both asteroids to be included in the system and the surroundings to be nothing. Because there are no surroundings dL_A/dt is 0. Therefore, L_Af = L_Ai. If this is the case, the angular velocity should be the same in the initial and final conditions. Is this true?
I then said that L_rot = Iω, and L_rot = r_cm1 X p_1 + r_cm2 X p_2. So I had the following equation:
Iω = r_cm1 X p_1 + r_cm2 X p_2.
Then I solved for ω,
ω = (r_cm1 X p_1 + r_cm2 X p_2)/I.
Is this correct reasoning? Are the initial and final angular velocities different? Should I consider a system with just one asteroid instead?
Thank you