A wire of the shape of y=ax² is rotating around its vertical axis with an angular velocity wo (see figure below). a point mass m is moving frictionlessly on the wire under the gravitational force. (a) Write down the Lagrangian in terms of x and i. (b) Derive the equation of motion. (c) At what value of @o, can the mass m stay at rest any where along the wire? y y=ax m
A wire of the shape of y=ax² is rotating around its vertical axis with an angular velocity wo (see figure below). a point mass m is moving frictionlessly on the wire under the gravitational force. (a) Write down the Lagrangian in terms of x and i. (b) Derive the equation of motion. (c) At what value of @o, can the mass m stay at rest any where along the wire? y y=ax m
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Transcribed Image Text:A wire of the shape of y=ax² is rotating around its vertical axis with an angular velocity wo
(see figure below). a point mass m is moving frictionlessly on the wire under the gravitational
force.
(a) Write down the Lagrangian in terms of x and i.
(b) Derive the equation of motion.
(c) At what value of @o, can the mass m stay at rest any where along the wire?
y
y=ax
m
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