Dynamics, Lectures 13 & 14: Oxford Mathematics 1st Year Student Lecture
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Summary of Linear Momentum Dynamics
The linear momentum (P) of a system of particles, when considered relative to its center of mass (G), satisfies DP/DT = sum of external forces, indicating that the translation of the center of mass is dictated solely by external forces, independent of internal interactions.
Torque from External Forces about an Arbitrary Point
The total external torque about an arbitrary point P is the sum of (r_i - X) cross F_i_external, where r_i is the position of particle i and X is the position of point P. This term represents the rotational effect of external forces on the system about point P.
Angular Momentum about the Origin and Center of Mass
When the reference point P is the origin of an inertial frame or the center of mass (G), the angular momentum equation simplifies significantly. If P is the origin, L_0 dot = tau_0_ext. If P is G, L_G dot = tau_G_ext, as the term involving the velocity of G and total momentum P vanishes.
