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Introductory Physics Homework Help
Show that the flywheel inside the train counteracts lean in a curve
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[QUOTE="Karl Karlsson, post: 6242608, member: 667628"] [B]Summary:[/B] Consider a train carriage rolling along a curve that forms a left turn on the track. The carriage speed is directed along the y-axis (into the plane of the paper) in the figure. The trolley will have a tendency to curl in the curve in the specified direction. A flywheel is inserted which rotates with a large angular velocity ω0 around its axis of symmetry along the x-direction. Decide whether ω0 should be directed in the positive or negative x direction to counteract the rolling of the carriage. [ATTACH type="full" alt="Skärmavbild 2019-10-03 kl. 18.47.02.png"]250686[/ATTACH] Consider a train carriage rolling along a curve that forms a left turn on the track. The carriage speed is directed along the y-axis (into the plane of the paper) in the figure. The trolley will have a tendency to curl in the curve in the specified direction. A flywheel is inserted which rotates with a large angular velocity ω0 around its axis of symmetry along the x-direction. Decide whether ω0 should be directed in the positive or negative x direction to counteract the rolling of the carriage. Motivation is required. Solution: [ATTACH type="full" alt="Skärmavbild 2019-10-03 kl. 18.47.36.png"]250687[/ATTACH] I understand the whole solution up to the last line. My reasoning why the vector w0 should be directed in the negative x direction: w1 is a constant. In order to [ATTACH type="full" width="99px" alt="Skärmavbild 2019-10-03 kl. 18.47.36.png"]250688[/ATTACH] something in the right must have the opposite direction compared to what it had before, this can also be seen from the cross product on line 5 in the solution. Since w1 is constant, it must be the angular momentum of the mass centra that has the opposite direction, when we calculated MG, the momentum of motion was directed along the x-axis, now it must be directed along the minus x-axis and hence the vector w0 must be directed in the negative x direction. Can anyone mathematically show why I'm wrong. Thanks! [/QUOTE]
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Show that the flywheel inside the train counteracts lean in a curve
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