Four identical masses (each size m) are attached to the corners of a square frame of...

  

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Four identical masses (each size m) are attached to the corners of a square frame of dimensions 2a x 2a. The frame is of negligible mass. Initially the system rotates in its plane with a = wê, with the CM at rest. We briefly fire a rocket thrusters in to the page at corner B, endowing the system with momentum -P2. As it happens, P 2mwa. (a) Find the new angular momentum L (relative to an origin at the CM) and spin , expressed in the a, ŷ, 2 basis. (b) Find the velocities of each of the four masses just after the thrust, and verify that the total momentum is -Pi. (c) Find the kinetic energy of the system. (d) How long will it take before the square again lies in an â- ý plane (granted, at a new z). A za D' Four identical masses (each size m) are attached to the corners of a square frame of dimensions 2a x 2a. The frame is of negligible mass. Initially the system rotates in its plane with a = wê, with the CM at rest. We briefly fire a rocket thrusters in to the page at corner B, endowing the system with momentum -P2. As it happens, P 2mwa. (a) Find the new angular momentum L (relative to an origin at the CM) and spin , expressed in the a, ŷ, 2 basis. (b) Find the velocities of each of the four masses just after the thrust, and verify that the total momentum is -Pi. (c) Find the kinetic energy of the system. (d) How long will it take before the square again lies in an â- ý plane (granted, at a new z). A za D'