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Let's say there is a solid cylinder floating in space and rotating about its axis of symmetry at rate $\omega$. At time t = 0 a force constant in magnitude is applied to the bottom of the cylinder. The force is parallel to the axis of symmetry and applied a distance r from it. From that moment forward, the force stays 'on' and its direction and point of application are fixed with respect to the cylinder. (In the second image below, the red vector represents the initial angular momentum, the blue vector represents the force, and the green vector represents the torque.)

Would the cylinder undergo precession (in addition to linear acceleration) or is the motion more complicated because the applied force is attached to the cylinder? I can see how for a precessing gyroscope always has the net torque perpendicular to $\frac{d\omega}{dt}$. I'm having trouble seeing if that would also be true here.

enter image description here vectors

Noah
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1 Answers1

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This is much like a spinning gyroscope on a table. In this case, the gyroscope is vertical. The gyroscope or cylinder will accelerate upward without tilting.

If the cylinder is tilted, the force applies a torque that tilts the axis of rotation. See Toppling of a cylinder on a block if you want more info on why.

Like a tilted gyroscope on a table, the cylinder will precess.

mmesser314
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