Final answer:
The angular momentum (L) of the object with position vector ra = (8, -8, 0) m and momentum vector p = (12, 13, 0) kg-m/s is 200k kg-m^2/s, indicating it points in the positive k direction.
Step-by-step explanation:
The angular momentum (L) of an object can be found by taking the cross product of its position vector (r) and momentum vector (p). The formula to calculate angular momentum is L = r x p, where r and p are vectors. Given the position vector ra = (8, -8, 0) m and momentum vector p = (12, 13, 0) kg-m/s, the cross product can be computed using the determinant method for vectors in three dimensions.
First, write the determinant with the unit vectors i, j, and k in the first row, the components of the position vector in the second row, and the components of the momentum vector in the third row. Then, expand the determinant to compute the cross product:
- The cross product in the i direction (ignoring i since it will be zero): (0)(0) - (-8)(0) = 0
- The cross product in the j direction (ignoring j since it will be zero): (0)(12) - (8)(0) = 0
- The cross product in the k direction: (8)(13) - (-8)(12) = 104 + 96 = 200
Therefore, the angular momentum La is (0i + 0j + 200k) kg-m2/s, or simply 200k kg-m2/s pointing in the positive k direction.