2005final - PHYSICS 321 FINAL EXAM May 4, 2005 NAME 1. [5...

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Unformatted text preview: PHYSICS 321 FINAL EXAM May 4, 2005 NAME 1. [5 pts] A particle of mass M moves in one dimension in the potential V ( x ) = a + bx where a and b are constants. Find all possible motions x ( t ). 2. [5 pts] The motion of a system with two degrees of freedom is described by the two coordi- nates x and y . The kinetic energy and potential energies are given by T = 1 2 [ x 2 + x y cos( x ) + (1 + t 2 ) y 2 ] V = x 2 + t y 2 Write the Lagrangian equations of motion. (But dont try to solve themsomeone might get hurt!) 3. [5 pts] A point mass m is located at a distance a from one end of a uniform wire of mass M and length b as shown. Find the gravitational potential energy of the mass. You may leave your answer in the form of a well-defined integralyou do not have to evaluate the integral. 4. [5 pts] A uniform disk of mass M and radius R is rotated about its diameterlike a coin spinning on its edge. Calculate the moment of inertia. 5. [5 pts] A satellite of small mass m is in a circular orbit of radius...
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2005final - PHYSICS 321 FINAL EXAM May 4, 2005 NAME 1. [5...

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