Download e-book for iPad: Advance Dynamics: Modeling and Analysis by A. Frank D'Souza

By A. Frank D'Souza

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4 ANGULAR MOMENTUM OF A SYSTEM OF PARTICLES ')t m2 '' \ First, we consider a single particle of mass m acted upon by a resultant force The particle has velocity ~ measured with respect to an inertial coordinate system Oxyz as shown in Fig. 12. The linear momentum of the particle ism~. The moment of the linear momentum vector about the fixed point 0 is x m-;. This is referred to as the angular momentum -vector H. of the particle about point 0 and is given by li. 11 Trajectory of an exploding projectile.

T! i +(h. t1- m 1 Xt m2 Y2 = mm (h. ,. 4 ANGULAR MOMENTUM OF A SYSTEM OF PARTICLES ')t m2 '' \ First, we consider a single particle of mass m acted upon by a resultant force The particle has velocity ~ measured with respect to an inertial coordinate system Oxyz as shown in Fig. 12. The linear momentum of the particle ism~. The moment of the linear momentum vector about the fixed point 0 is x m-;. This is referred to as the angular momentum -vector H. of the particle about point 0 and is given by li.

Hence, v 2 jv1. The forces acting on each of the masses are shown in Fig. 15. The tension in the cable is a constraint force and does no work. Also, forces m 1 g, m 2 g, N 1 , and Nz do no work and are ignored. When mass m 1 has moved a distance d, mass m 2 moves a distance jd. Hence, the total work done is given by: work Pd- F 1d- Fzjd But F 1 pNt. Fz pN2 , N 1 m 1g, and N 2 mzg. 48) and it is employed in computing the kinetic energy. The generalization of this principle to a system of n particles is straightforward.

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Advance Dynamics: Modeling and Analysis by A. Frank D'Souza


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