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In short, you are to think of the direction of the torque as pointing along the axis of the rotation it would induce in a rigid body initially at rest. But if the conception of torque as a vector out of the page seems artificial, that's because it is. Torque is not fundamentally a quantity that is a vector but a directed plane or directed area. Such an ...

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There are probably lots of duplicates, so my apologies, but for clarity I will try a short answer, as the graphic from Wikipedia is particularly illustrative. The torque is perpendicular, ( orthogonal) to the other two vectors, so it could be the line where the hinges are located, depending on the direction of the other two forces. From Wikipedia ...

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However, Robot A moves at a speed 9 times faster than Robot B. Are you stating this as a given, or do you presume it arises from the consequence of the gearing? If so, it is incorrect because an engine does not deliver a constant speed, but instead a maximum power. The higher geared robot will have a larger load on the engine, reducing the speed it can ...

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You can think about this in two different ways. One way is to look at the initial and final angular momentum. If you go from $L\cdot(0,1, 0)$ to $L\cdot(1,0,0)$ you need to remove the $Y$ component and add the $X$ component. If you just calculate the difference in the angular momentum, then you get $$\Delta L = L\cdot (1,-1,1)$$ which would immediately ...

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I believe the issue is that the sketch doesn't show all forces acting on the bar. (My guess is that this is a question concerning only rotation about the y-axis) There must be forces at point A as well. The bar seems fixed at this point so that a torque will appear here to balance the others in order to keep no rotation. The torque 159 Nm comes from force \$...

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