Introduction to Classical Mechanics

Newton s second law of motion, F = d mw)/dt, relates the total force F acting on an object with its time rate of change of momentum p, where p = mv. The force F acts through the center of mass of the object. Newton s second law allows us to determine the trajectory of the center of mass of any object relative to a space-fixed (laboratory) or inertial coordinate system. Similarly, the torque acting on an object. To, about some reference point 0 is equal to the time rate of change of the angular momentum Lq of the object about the reference point, i.e., To = d Loldt. 

As shown below, the motion of an arbitrarily shaped body, such as a structured molecule, can be decomposed in terms of translational motion of the center of mass of the molecule (F = dp/df) and rotation of the molecule about its center of mass (Tg = dLc/df). It is to be noted that in writing the force and torque equations, all vector components are with reference to an inertial or space-fixed (laboratory) frame. 

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