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Sol_Problem_of_the_Week_–_11 - Solution...

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Solution Problem of the Week – 11 Here is a device consisting of four heavy metal balls connected together by rods whose mass is negligible. Its center of mass is moving to the right with speed 10 m/s, and it is rotating counterclockwise with angular speed 45 radians/s. (Use the usual convention for the coordinate axes: x to the right, y towards the top of the page, and z out of the page towards the reader.) (a) Calculate the translational angular momentum of the device relative to location A . The translational angular momentum about point A is given by: ! L trans , A = ! R CM , A ! ! P CM where ! R CM , A is a vector from point A to the location of the CM at the instant shown in the figure. Direction: The cross product on the right hand side gives the direction of the translational angular momentum into the page, i.e., along the negative z direction. Magnitude: ! R CM , A = .36,.30,0 m ! P CM = 10 kg ! 10,0,0 m / s = 100,0,0 kg ! m / s ! L trans , A = 0,0, ! 30 kg " m 2 / s , ! L trans , A = 30 kg ! m 2 / s
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