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When you apply this force, it will be transmitted to every joint, so each segment will behave as under a field making them turn. A way to see this is imagine only one segment tied to a fixed point: when you apply a force to the free end, what do you think the reaction force is in the fixed point? The difference now is that since each point joining two ...

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Since a system must obey the law of momentum conservation, the center of mass of a system (which can be made of one or many bodies) must have constant velocity if no external force is applied. Hence, a body can rotate around its center of mass, or it can rotate around any other point, but only if under the influence of an external force. Therefore one can ...

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When calculating gravitational potential energy the only thing that matters is the position of the centre of gravity. So if the vertical position of the centre of gravity changes by $\Delta h$ the gravitational potential energy changes by $\Delta V = mg\Delta h$.

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In 2D, torque is $\tau = (r \sin \phi) F = r ( F \sin \phi)$. These are equivalent statements. You either consider the perpendicular distance to the line of action of $F$, or the perpendicular component of $F$ along $r$. Either way the result is the same. It really doesn't matter how you interpret this expression, as both ways are valid. In 3D, torque is ...

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A way to understand this is as follows . According to a definition, moment arm is the perpendicular distance from the axis to the line of action of force and the lever arm is the length of the line that connects the axis to the point of action of force. Hence, when the force is perpendicular to the lever arm, the lever arm and the moment arm coincide. For ...

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It will spin about its axis. In general terms, if you attach a flywheel to a big motor in space and turn it on, the flywheel will spin in one direction with some angular velocity, and the motor and whatever is attached to the motor will spin in the opposite direction with a different angular velocity. This is the basic principle behind a reaction wheel. ...

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Indeed. It is due to the law of conservation of angular momentum. The angular momentum of the rotating element within the motor will exactly cancel that of the rest of the motor, thereby giving zero net angular momentum, as with the initial conditions.

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Allowing the bar to pivot about point G, you will see that R1 (if it was the only force) would rotate the bar clockwise and R2 (by itself) would rotate the bar counterclockwise. The direction of rotation is determine by the direction of the force (up or down) and where it acts in relation to the pivot (right or left).

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The casing will spin in the opposite direction. That is the principle of reaction wheels.

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I would do a hand analysis at first. You have two torques on the arrow. One is the drag torque, which is maximum when the arrow is transverse to the orbital velocity, as in your initial condition. The second is gravity gradient torque, which will be maximum when the arrow is horizontal. Compute each of these for your arrow. If one is much greater than ...

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