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why the torque is negative in this case ? the question ask for determine the angle of twist of gear C with respect to B .

We have to 'fix' the B , and determine the twist of C ? So , imagine that we cut off the shaft and gear , now only left with gear B and gear C connected by a shaft . So , when B is fixed , the gear C rotate , with the direction of torques pointing to the left ( by using right hand grip rule ) , So , the finger point towards B , so it's negative ? 11

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Negative and positive are essentially arbitrary and are really just to differentiate the directions of the moments and forces. You can chose your positive y direction to be facing down for example, if that's how you want to arrange your coordinates.

The standard orientation is right and up are both positive coordinates. If we assume they are using standard coordinates; then it should be negative using the right hand rule. You yourself said when using the right hand rule that your thumb pointed left. That is generally considered the negative x direction, therefore the moment is considered negative.

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  • $\begingroup$ i just wanna verify that [ the question ask for determine the angle of twist of gear C with respect to B . We have to 'fix' the B , and determine the twist of C ? So , imagine that we cut off the shaft and gear , now only left with gear B and gear C connected by a shaft . So , when B is fixed , the gear C rotate ] is my concept correct ? $\endgroup$ – kelvinmacks Jan 6 '17 at 13:11
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they are not opposing. Their rotation is a ratio regarding the number of teeth n1/n2. If you fix b so that there is torsion I think you're moving in the wrong direction. The torque* down the shaft is constant. The torque is relative to the diameter of the gear i.e. F*r = T. The angle is simply geometric unless it is restricted by an outside torsional force. They both rotate in the same direction but with different torque.

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