By Haire, M.J.; Oak Ridge National Laboratory.; United States. Dept. of Energy.; United States. Dept. of Energy. Office of Scientific and Technical Information
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38) where rk is the position of the kth particle, Pk its instantaneous momentum, and Fk the instantaneous force acting on it. 5. Example. In this example, we show that the torque on a collection of three particles is caused by external forces only. The torques due to the internal forces add up to zero. 1 when we learn how to manipulate summation symbols. 38) reduces to Each force can be divided into an external part and an internal part, the latter being the force caused by the presence of the other particles.
Cylindrical: (0, Ie, 4), (2, Jr, 0), (0, 217, -18), (1, 3Jr /4, -2), (1,2,3), (1,0,0). 16. 21). 40 1. 17. Points P and p' have spherical coordinates (r, (), cp) and (r', ()', cp'), cylindrical coordinates (p, cp, z) and (p', cp', z'), and Cartesian coordinates (x, y, z) and (x', y', z'), respectively. Write Ir - r'1 in all three coordinate systems. 2) with a = Ir - r'1 and r and r' written in terms of appropriate unit vectors. lS. 24) is independent of where we choose the origin to be. 24). 19.
1558 2 , a Erp a = E . 0567erp . 0152erp . 2268erp . 0294 2keq . a The choice of Cartesian coordinates was the most straightforward one, but one can choose any other coordinate system to calculate the field and find the components in any • other set of unit vectors. The reader is urged to try the other choices. 1. Find the equation of a line that passes through the following pairs of points: (a) (1,0,1) and (-1,1,0). (b) (2,2, -1) and (-2, -1, 1). (c) (1,1,1) and (-1,1, -1). (d) (1,1,1) and (-2, 2, 0).