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1.1.1a central force? [3] 1.1.2a non-central force? [3] 1.2 From their characteristics, identify three differences between central and non-central forces [3] 1.3 Give one example of 1.3.1 a central force [1] 1.3.2 a non-central force [1] QUESTION 2: THE LAGRANGIAN [10 MARKS] The position of a free particle in a frame of reference for a given system at any time may be represented by a vector r = r (x, y, z). 2.1 If the system has five independent particles, how many coordinates would be required determine the configuration of the whole system? Explain how you arrived at your answer. [4] 2.2 What is meant by the generalized coordinates of a given system? [2] 2.3 Given that the generalized coordinates of a system are denoted by qi where i = 1, 2, ..., n, write down in terms of the 2 Page HPSG031 REVISION TEST 2 / APRIL 2022 generalized coordinates the general form the position vector of the particles of the system. [2] 2.4 How many generalized coordinates do you require for a free particle in a Cartesian coordinate reference system? Name them.