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Physics 325 Spring 2011 Homework 8

# Physics 325 Spring 2011 Homework 8 - Physics 325 Spring...

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Physics 325 Spring 2011 Homework 8A Name: ____________________________ Due: Apr 13, 2011 by 9am (lecture or 325 box) 1. (10 points) A particle of mass m is constrained to move on a circle of radius R . The circle rotates in space about one point on the circle, which is fixed. The rotation takes place in the plane of the circle and with constant angular speed . In the absence of a gravitational force, show that the particle’s motion about one end of a diameter passing through the pivot point and the center of the circle is the same as that of a plane pendulum in a uniform gravitational field. 2. (10 points) A smooth wire is bent into the shape of a helix, with cylindrical polar coordinates R and z  , where R and are constants and the z axis is vertically up (and gravity acts vertically down). Use z as your generalized coordinate. (a) Write down the Lagrangian for a bead of mass m threaded on the wire.

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