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# 2 Y I ... and you're eager to begin swinging it around various axes, but you're not sure how big a motor you'll need

## 2 Y I ... and you're eager to begin swinging it around various axes, but you're not sure how big a motor you'll need to get the swinging performance you desire. The object has uniform density p, and if you define coordinate directions as shown with the point (x, y, z) = (0,0,0) at the object's bottom-left corner, then the object occupies the region in which 0 x 1, 0 y 1-x, where x, y, and z are measured in meters. 0 x x, In terms of p, compute the object's mass and the components of its inertia matrix. Out[2]= z, x + y, xy, xz, yz} volint/@ {1, y + z, x + z 1 - ' 5 1 1 - 4 72' 9' ' - 8 , 4 105 , 1 24 ' 2 105 ;} I Y 8 In terms of p, what's the rotational inertia of the larger composite object with respect to the z axis? Suppose that you spin the larger composite object around the z axis with angular velocity wk, where w is a positive constant. In terms of p and the angular speed w, what's the object's angular momentum with respect to this axis? What contribution does the original, solitary object make to this angular momentum? Suppose that you spin the composite object with angular velocity wk around the axis that passes through the points (x, y, z) = (-1m,-1m, -3m) and (x, y, z) = (-1m,-1m, 3m), shown in this color here: I Y In terms of p and w, what's the object's kinetic energy? Make sure your answer has the correct units. If the composite object is spinning with angular velocity wok around that external axis, then when it's situated as shown in the figure above, what are the velocity and acceleration of the point on the object located at (x, y, z) = (1m, 0m, 1m)?

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