c) d) a) b) 3. Consider two uniform rods of equal length and mass, AB and CE, welded together at point D (Figure 3A). The assembly is supported by bearings at A and B. Each rod has a mass of 4 [kg] and the dimensions shown in Figure 3A. Moment of inertia for an individual rod is zero along its long axis (i.e. 1,-0) and 1,=1=ml about its other two axes. 12 Figure 3A 75 mm 225 mm (0) 225 mm 75 mm Determine the inertia tensor for the entire assembly with respect to its principal axes. [5 marks] At the instant shown, the assembly has an angular velocity of 13 [radians/s] acting along rod AB as shown. Calculate the angular momentum vector about point D, F, with respect to the fixed frame of reference axes, xyz. [5 marks] Calculate the kinetic energy of the assembly. [5 marks] Consider the rigid body in Figure 3B constrained to rotate about a fixed axis that runs along its z-axis. If the body has an angular velocity of @ and an angular acceleration of a, derive the following expression for the three- dimensional moments acting on the body about point O: