A boom on a large space station is used to launch small pods into space, see Figure 4. The boom of mass m = 15 kg can be modelled as a thin rod of length LB = 4 m while the pod has a mass of m, = 1.5 kg, a radius of gyration k = 0.06 m and its center of mass is at a distance L, = 3.8 m, see Figure 4. The pod is attached to the boom with an electromagnet that can be released when it has attained a suitable velocity. To launch the pod, a constant moment Mo = 20 N-m is applied to the boom for a period of t = 3 s after which the pod is released. a) Determine the polar second moment of mass of the boom and pod about the pivot. (40% points) b) Determine the speed of the pod as it leaves the space station. (60% points) c) If the center of mass of the space station is at a distance 50 m from the boom pivot and has a mass mes = 25000 kg and a radius of gyration ks = 35 m, determine the change in angular speed of the space station after the pod has launched. (15% bonus points) Note the polar second moment of mass I Grod about the center of mass for a thin rod is mBL 12 I Grod = (3) Pivot Mo, L LB Figure 4: Space station pod launcher. Boom Pod