1. 1.A (17 points) The figure shows three particles of the same mass me 1 Kg and
ID: 1644772 • Letter: 1
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1. 1.A (17 points) The figure shows three particles of the same mass me 1 Kg and the same constant speed ve2m/s. The arrows in the figure indicate the corresponding velocity vectors. The dashed lines are shown just for reference. Notice the five points P, O, R, and T form a square with point L at the center. The figure also shows the unit vectors i and j. lv PO 1 m .2 :V TR a) Calculate the vector angular momentum of the three-particle system with respect to reference with origin at T. Indicate its magnitude and corresponding unit vector. Show explicitly all your analytical calculations (including the contribution to the total angular momentum from each particle, the vector positions and vector velocities of the particles, the determinant method to calculate the vector product, etc.) b) Calculate the vector angular momentum of the three-particle system with respect to the reference with origin at L Show explicitly all your analytical calculations (including the contribution to th total angular momentum from each particle, the vector positions and vecto velocities of the particles, the determinant method to calculate the vect product, etc.)Explanation / Answer
1. (A) angular momentum = r x mv
m1 = m2 = m3 = 1 kg
v1 = 2 i , v2 = 2 j , v3 = 2i
About T,
r1 = -i + 2j
r2 = 2i + j
r3 = 3 i
| i j k |
L1 = | -1 2 0 | = -4 k
| 2 0 0 |
| i j k |
L2 = | 2 1 0 | = 4 k
| 0 2 0 |
| i j k |
L3 = | 3 0 0 | = 0 k
| 2 0 0 |
L = L1 + L2 + L3 = 0
(b) About L ,
r1 = -2i + j
r2 = i
r3 = 2i -j
| i j k |
L1 = | -2 1 0 | = -2 k
| 2 0 0 |
| i j k |
L2 = | 1 0 0 | = 2 k
| 0 2 0 |
| i j k |
L3 = | 2 -1 0 | = 2 k
| 2 0 0 |
L = L1 + L2 + L3 = 2 k
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