Question

1.1 A bead of mass m slides without friction along a straight wire AB, under the influence of the Earth's gravitational field. The perpendicular distance from the center of the wire C to the origin O is the constant distance d. The line OC rotates with constant angular velocity around a fixed horizontal axis through O and perpendicular to the wire. Initially the wire AB is horizontal and the bead is positioned at C with zero velocity. (a) Derive the Lagrangian for this system using appropriate generalized coordinates. (b) Establish the equation of motion for the bead and solve it.

          1.1
A bead of mass m slides without friction along a straight wire AB, under the
influence of the Earth's gravitational field. The perpendicular distance from the
center of the wire C to the origin O is the constant distance d. The line OC rotates
with constant angular velocity around a fixed horizontal axis through O and
perpendicular to the wire. Initially the wire AB is horizontal and the bead is
positioned at C with zero velocity.
(a) Derive the Lagrangian for this system using appropriate generalized
coordinates.
(b) Establish the equation of motion for the bead and solve it.

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1.1
A bead of mass m slides without friction along a straight wire AB, under the
influence of the Earth's gravitational field. The perpendicular distance from the
center of the wire C to the origin O is the constant distance d. The line OC rotates
with constant angular velocity around a fixed horizontal axis through O and
perpendicular to the wire. Initially the wire AB is horizontal and the bead is
positioned at C with zero velocity.
(a) Derive the Lagrangian for this system using appropriate generalized
coordinates.
(b) Establish the equation of motion for the bead and solve it.

Added by Anthony D.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Krishna J

Step 1

In this case, it is convenient to choose the angle θ between the line OC and the vertical axis as our generalized coordinate. The position of the bead can be described by the coordinates (x, y), where x is the horizontal distance from the origin O and y is the Show more…

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1.1 A bead of mass m slides without friction along a straight wire AB. under the influence of the Earth's gravitational field. The perpendicular distance from the center of the wire C to the origin O is the constant distance d. The line OC rotates with constant angular velocity around a fixed horizontal axis through O and perpendicular to the wire. Initially the wire AB is horizontal and the bead is positioned at C with zero velocity. (a) Derive the Lagrangian for this system using appropriate generalized coordinates. (b Establish the equation of motion for the bead and solve it B

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