Q5 (20pt) Motion in non-inertial frame using Lagrangian A bead of mass m is constrained to slide along a thin, circular hoop of radius R that rotates with a constant angular velocity w in a horizontal plane about a point on its rim as shown below. cut (a) Use Lagrangian method to find the differential equation of motion for the bead in p. (b) The motion of the bead can be considered in the rotating frame of which the origin coincides with the center of the circle. Verify your answer of (a) by direct application of the equation of motion in rotating frame: Fnet _Raxi -ax (w x r) - 20 xu, m Hints: (1) use polar coordinate (r, ) in the rotating frame (the acceleration vector in the rotating frame, dy, in polar form can be found in Example 1.8 in the textbook), and (2) think about what the net force along the p direction, Fo, is. w Xr R. ct >X