By Cahn S.B., Nadgorny B.E., Yang C.N.
So as to equip hopeful graduate scholars with the information essential to go the qualifying exam, the authors have assembled and solved commonplace and unique difficulties from significant American universities - Boston college, collage of Chicago, collage of Colorado at Boulder, Columbia, college of Maryland, collage of Michigan, Michigan kingdom, Michigan Tech, MIT, Princeton, Rutgers, Stanford, Stony Brook, collage of Wisconsin at Madison - and Moscow Institute of Physics and expertise. quite a lot of fabric is roofed and comparisons are made among related difficulties of alternative faculties to supply the scholar with adequate details to suppose cozy and assured on the examination. advisor to Physics difficulties is released in volumes: this publication, half 1, covers Mechanics, Relativity and Electrodynamics; half 2 covers Thermodynamics, Statistical Mechanics and Quantum Mechanics.
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Extra resources for A Guide to Physics Problems. Mechanics, Relativity, and Electrodynamics
The rod-and-ball system rotates with constant angular velocity TLFeBOOK 20 PROBLEMS a) Set up the equation of motion, neglecting the weight of the arms and rod. Use as variable the distance between the sleeves. 34 Double Pendulum (Stony Brook, Princeton, MIT) The double pendulum consists of a mass suspended by a massless string or rod of length from which is suspended another such rod and mass (see Figure P. 34). TLFeBOOK 21 MECHANICS a) Write the Lagrangian of the system for b) Derive the equations of motion.
28 Sliding Ladder (Princeton, Rutgers, Boston) A ladder of mass and length stands against a frictionless wall with its feet on a frictionless floor. If it is let go with initial angle what will be the angle when the ladder loses contact with the wall (see Figure P. 28)? 29 17 Unwinding String (MIT, Maryland (a,b), Chicago (a,b)) A point mass is attached to a long, massless thin cord whose other end is attached to a fixed cylinder of radius R. Initially, the cord is snugly and completely wound up around a circular cross section of the cylinder, so that the mass touches the cylinder.
A car rolling on steel rails is released from rest at New York, and rolls through the tunnel to San Francisco (see Figure P. 10). TLFeBOOK MECHANICS 9 a) Neglecting friction and also the rotation of the Earth, how long does it take to get there? Take the gravitational acceleration and the radius of the Earth R = 6400 km. b) Suppose there is now friction proportional to the square of the velocity (but still ignoring the rotation of the Earth). What is the equation for the phase space trajectory?