Just like the reaction of the weight of a body is a force acting on Earth towards the body, where and in what direction does the reaction of a gyroscopic force act?
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$\begingroup$ Do you think the reaction force will be different for a gyroscope compared to another body? $\endgroup$– ChrisMMar 21, 2015 at 21:39
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$\begingroup$ Now you have clarified your question I think it is a duplicate of physics.stackexchange.com/q/271/26969 $\endgroup$– FlorisMar 22, 2015 at 20:25
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2 Answers
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There is no "gyroscopic force". The best you can say is that there is a "reaction torque" when you apply a torque to a gyroscope. When a torque (which is a vector $\vec\Gamma$) is applied to a gyroscope with angular momentum (also a vector $\vec L$) the resulting motion of the gyroscope is a precession - the tip of the angular momentum vector rotates along the direction of the torque vector.
If you attempt to move a gyroscope such that its axis of rotation has to change, the reaction will be opposite to the direction of the torque you apply.
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1$\begingroup$ If you hang a wheel to a string, hold it upright such that the axis of the wheel is perpendicular to the vertical and give the wheel a rotation; the wheel rotates about the string.. that's precession okay. But why does the axis of the wheel not become parallel to the vertical just like it would have become had the wheel not been rotating? I hope the question is clear.. $\endgroup$ Mar 22, 2015 at 5:51
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1$\begingroup$ @PriteeshRanjan Whether the wheel be precessing or with the axis hanging vertically, the two forces on the wheel - weight downwards and tension from the string upwards - are exactly the same, equal and opposite in magnitude, in both cases. In the spinning wheel case, it is simply that there can be a nett torque from these forces (nonzero horizontal separation between their parallel lines of action, through string and through the COM) that does not force the wheel's axis to be vertical, but instead makes the angular momentum change with time ("angular acceleration") i.e. the wheel precesses. $\endgroup$ Oct 3, 2015 at 7:44
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i think the gyroscopic reaction torque is in the ratio of sine of angular momentum to the force applied. point to be noted that reaction force is less experienced when the gyro rotates at a lower rpm.>
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1$\begingroup$ I'm not sure how this answers the question of location and direction of the reaction force. $\endgroup$ Mar 5, 2016 at 15:27