A small flywheel is spinning around a horizontal axle with constant angular spee

Question

A small flywheel is spinning around a horizontal axle with constant angular speed. Neglect any friction. The axle itself is free to rotate in any direction (this could for example be achieved through a Cardan suspension). Initially the axle points into the x-direction. You would like to rotate the axle by 90 degrees so that it points into the y-direction. Hence you apply a force in the x-y-plane pointed perpendicular to the axle. What will happen? Newton's Second Law tells us that if a force is applied perpendicular to the axle it will start to move in the direction of the force. Hence it will swing around from the x-direction towards the y-direction as intended. The rotating flywheel has angular momentum which points along the axle (i.e. the x-axis). Angular momentum is conserved, so you can not simply change the direction of the axle. If you want to change the direction of motion you first need to stop the flywheel, then rotate the axle to point in y-direction, then spin it up again. So when you apply the force as described the axle will not move at all. A force in the x-y-plane means the torque on the axle is perpendicular to the x-y-plane. The torque changes the angular momentum of the flywheel. Originally the angular momentum points into the x-direction and the torque will move it OUT of the x-y-plane, perpendicular to the direction of the force. Thus the axle will not move into the y-direction as intended but away from the x-y-plane None of the above is correct.

Explanation / Answer

a force in the x-y plane means the torque on the axle is perpendicular to the x-y plane the torque changes the angular momentum of the flywhewel .originnaly the angular momentum points into the x direction and the torque will move it out of the x-y plane perpendicular to the direction of force

torque will not act.

hence option c is right answer.

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