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(Q4) [10 points] A particle is constrained to move on a frictionless circular rotating Wire that has an angular velocity in about the vertical. [see Fig. 2) (a) Find the Lagrange's equation of motion. (b) Find the equilibrium positions of the particle. (c) Expand the angle 6' around each of the equilibrium positions 90 as e = 9 I99 and nd the the equation of motion for E for each equilibrium position. (Q5) [5 points] Calculate the components of angular velocity of a rigid body in terms of Euler angles and its time derivatives, in the body frame of reference