Problem & Given: The figure shows a free-body diagram for a quadcopter drone with a weight mg = 160 N. For rotations about the z-axis (indicated by ), the moment of inertia for the entire drone (including the four identical motor/blade units) about its mass center O is 1.020 kg-m?. For rotations about the x-axis (indicated by ) and for rotations about the y-axis (indicated by ), the drone's moment of inertia about 0 is 0.060 kg-m?. The motor/blade units are each located at a distance of 0.25 m from O, and each blade has a moment of inertia of 0.008 kg-m? for rotations about the vertical axis. Notice that blades 1 and 3 rotate counterclockwise, while blades 2 and 4 rotate clockwise. Each motor/blade unit also generates a vertical thrust; for simplicity, you can assume that F} = |0.80 w;| N k, where i = 1,2,3,4. Initially, the drone is hovering in place in the air with all four blades rotating such that &; = @3 = 50 g-';':E and W, = @y = 50 %;.f(. The drone itself is not rotating. Find: Listed below are three different scenarios for changing the angular velocities of the blades. For each change, indicate what the resulting motion of the drone will be by calculating an appropriate kinematic quantity (which could be either an acceleration of the center of mass, an angular velocity or angular acceleration about one of the rotation axes of the drone, or a combination of these). Also, describe in words how the drone will move after this change. a) @y = Wy = 45 7% and &, = @, = 45 %k, 2ec sec 58C b] E}'I = C'_L'.S 45%& andaz = a4 _SUEE. )@y = 45 20K, @y = 55 24K and @, = @, = ~50 k. Sec e