The Indirect Effect of the Internal Forces on the Linear Angular Momentum of A System of Particles

It is demonstrated that if the vector sum of the external forces and the total external torque are functions of all the positions and the velocities of the particles, the internal forces will affect indirectly the linear momentum and the angular momentum of a system of the particles through the and. In order to ensure that the internal forces have no effect on the and of the system, the external forces must be restricted to a linear function of and. Some examples which show that internal forces do affect the motion of the center of mass and the angular momentum of the system were discussed.

It is demonstrated that if the vector sum Fext of the external forces f_iext and the total external torque N^ext are functions of all the positions r_i and the velocities v_i of the particles, the internal forces will affect indirectly the linear momentum P= P_CM and the angular momentum L of a system of the particles through the r_i and v_i. In order to ensure that the internal forces have no effect on the P and L of the system, the external focces must be restricted to a linear fun- .ction of m_ir_i and m_iv_i Some examples which show that internal forces do affect the motion of the center of mass and the angular momentum of the system were discussed.