The mechanism for a car window winder is shown in the figure. Here the handle turns the small cog C, which rotates the spur gear S, thereby rotating the fixed-connected lever AB which raises track D in which the window rests. The window is free to slide on the track. If the handle is wound with angular velocity ω_c, determine the speed of points A and E and the speed v_w of the window at the instant θ.

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Given: @c = 0.5 Oc rad S 8 = 30 deg TA = 200 mm rc = 20 mm rs = 50 mm