Need help calculating the initial and final angular momentum Thank you junk.f Sp

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Need help calculating the initial and final angular momentum

Thank you

junk.f Space junk C B Vjunk.i Usatellite,i Satellite (z out of page) A spherical satellite of radius 4.8 m and mass M 195 kg is originally moving with velocity usatellite i m/s, and is originally rotating with an angular speed 1 = 2 radians/second in the direction shown in the diagram. A small piece of space junk of mass m = 4 kg is initially moving toward the satellite with velocity Ujunk,i- m/s. The space junk hits the edge of the satellite at location C as shown in the diagram, and moves off with a new velocity Ujunk f= -1300, 510, 0 > m/s. Both before and after the collision, the rotation of the space Junk is negligible MOMENTUM After the collision, what is the final momentum of the satellite? psatellite,f = | S | kg.m/s What is the final velocity of the satellite? osatellite,f = | d 2970,-10.5,0 m/s ANGULAR MOMENTUM Assuming the density of the satellite is uniform throughout, what is the moment of inertia of the satellite? (The moment of inertia of a uniform-density sphere is (2/5)MR2.) What is the initial rotational angular momentum of the satellite, around location D (its center of mass)? (Be sure your signs are correct) satellite,i kg m2/s 1800 kg m Which of

Explanation / Answer

Satellite radius - 4.8
Satellite mass - 195
Satellite velocity - <3000, 0, 0>
Angular speed - 2 rad/sec
Space junk mass - 4.1kg
Space junk initial velocity - <-2600, 0, 0>
Space junk final velocity - <-1300, 510, 0>

Final momentum of satellite
<3000*195 - 2600*4 + 1300*4, -510*4, 0>
<579800, -2040, 0>

Final velocity of satellite
<579800/195, -2040/195, 0/195>
<2973.33, -10.46, 0>

Moment of inertia of satellite
I = (2/5)MR^2
I = (2/5)*195*4.8^2
I = 1797.12

Initial rotational angular momentum
L = I x w
L = 1797.12*2
L = <0, 0, -3594.24>
Angular momentum is in the z direction and it is negative because the satellite is spinning clockwise.

(r_perp) is the same when the space junk is at locations A, B, and just before getting to C.
xp_y - yp_x is the same when the space junk is at locations A, B, and just before getting to C.
The translational angular momentum of the space junk is the same when the space junk is at locations A, B, and just before getting to C.

Initial translational angular momentum of space junk
L = I x w
L = m*v*r
L = 4*-2600*4.8
L = <0, 0, 49920>
Angular momentum is in the z direction and positive because of right hand rule

Final translational angular momentum of space junk
L = r x p
r = <0, 4.8, 0>
p = <-4800, 2040, 0>
r x p = <4.8*0 - 0*2040, 0*0 - 0*-4800, 0*2040 - 4.8*-4800>
= <0, 0, 23040>

Final rotational angular momentum of satellite
Lsatellitef = Ljunki - Ljunkf + Lsatellitei
= <0, 0, 49920> - <0, 0, 23040> + <0, 0, -3594.24>
= <0, 0, 23285.76>

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