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lets remind ourselves what these equations look like for a single particle if you have a single particle of mass m and you know the resultant force acting on this particle then the acceleration is just obtained by Newtons second law the total force equals mass times acceleration a what does this equation look like when you get to a system of particles and then a rigid body well lets start with a system of particles before we can define Newtons second law for a system of particles we must first define the center of mass the picture on the right hand side shows you a set of particles P 1 P 2 and so on lets assume that we can write position vectors P 1 P 2 P I for each of these particles lets denote the mass of the ith particle by M sub I we can now compute the average position vector by weighting each position vector with the appropriate mass so the equation you see here mi times TI is essentially the weighted sum of all the position vectors you divide that by the total mass m and
