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MIT16_07F09_hw11

# MIT16_07F09_hw11 - NAME Massachusetts Institute of...

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NAME : . . . . . . . . . . . . . . . . . . . . . Massachusetts Institute of Technology 16.07 Dynamics Problem Set 11 Out date: Nov. 14, 2007 Due date: Nov. 21, 2007 Time Spent [minutes] Problem 1 Problem 2 Problem 3 Problem 4 Study Time Turn in each problem on separate sheets so that grading can be done in parallel

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Problem 1 (10 points) Question 1 10 points A rectangular plate of mass M , length b and height a is fixed to a massless rod through is center of mass and the corners of the plate as shown. The rod is supported at two points separated by a distance L as shown. the plate rotates with the rod with an angular velocity ω . a.) Is the axis of rotation a principal axis? b) What is the angular momentum of the plate? Make a sketch of the angular momentum vector relative to the position of the plate. c) What forces are must be exerted by the supports? Give a formula for the forces in the two supports as a function of time. d) If the rod were not massless but had a mass M r , a radius R 0 and a length L 2 , how would your answer change?
Problem 2 (5 Points) Control of angular orientation and angular momentum are important in satellite operation. a) Consider first, satellite orientation. Satellite orientation is controlled by internal ”momentum wheels”. These are discs mounted and connected to the body of the satellite by an electric motor (driven by solar cells.) For simplicity consider the momentum wheel to be mounted at the center of mass of the satellite with its axis along a principal axis of the satellite. If the moment of inertia of the satellite along this axis is I S , and the moment of inertia of the momentum wheel is I W , what is the relation between the angular change of the momentum wheel Δ θ W and the angular change of the satellite Δ θ S . If the satellite arrives in orbit after launch and it is upside down, how can it be turned over θ S = π )?

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