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enter image description here

In rod reference frame:

  1. origin is center of the rod,
  2. pitching axis is coinciding with the rod
  3. external torque is applied in rolling axis

If a torque is applied to non-rotating object(the rod and the spheres), always in the same magnitude and a wheel is rotating always(not sliding to the right or the left)at the center of the rod connecting spheres as shown on the picture,

assuming:

  • the wheel rotates around the rod which is coinciding with angular velocity vector of the wheel, bearings are frictionless

  • this experiment is realized in a vacuumed gravity-free place

  • rod mass is ignored, and for simplicity you can assume sphere mass is a point mass with some value

  1. how will torque be shared between the wheel and spheres?

  2. as a result of torque applied to the wheel, in addition to rotation around rolling axis, the wheel will try to rotate around yawing axis due to gyroscopic effect but it will also try to rotate spheres, what will be result of this fact?

If you explain behavior of this object based on reference frames i would be pleased.

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  • $\begingroup$ Please, add some details: is there an hinge between the wheel and the rod connecting the two masses? Is this system constrained to the ground? If not, could we assume that weight is negligible? $\endgroup$
    – basics
    Commented May 23 at 17:04
  • $\begingroup$ The rod makes a torque to the wheel as it attempts to move obliquely, but I am not sure if that is what you are asking $\endgroup$
    – Pato Galmarini
    Commented May 23 at 19:52
  • $\begingroup$ Try expressing every state variable as a function of angular momentum. $\endgroup$
    – g s
    Commented May 23 at 19:54
  • $\begingroup$ So basically the entire thing will rotate clockwise as seen from above, and the wheel will keep spinning along the rod axis $\endgroup$
    – Pato Galmarini
    Commented May 23 at 20:04
  • $\begingroup$ I meant about, not along $\endgroup$
    – Pato Galmarini
    Commented May 23 at 20:14

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