By Sidney B. Cahn, Boris E. Nadgorny, C.N. Yang
In an effort to arm hopeful graduate scholars with the data essential to go the qualifying exam, the authors have assembled and solved common and unique difficulties from 4 significant American universities and Moscow Phys-Tech. quite a lot of fabric is roofed and comparisons are made among related difficulties of varied faculties to supply the scholar with sufficient details to believe cozy and assured on the examination.
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Extra info for A Guide to Physics Problems: Mechanics, Relativity, and Electrodynamics
Write down the Lagrangian in terms of the generalized PROBLEMS 18 coordinates and Identify two conserved quantities and express them as functions of and Which way does the cylinder spin? 30 Six Uniform Rods (Stony Brook) Six equal uniform rods, fastened at their ends by frictionless pivots, form a regular hexagon and lie on a frictionless surface. 31 19 Period as Function of Energy (MIT) A particle of mass moves in a one-dimensional potential where A is a constant. 32 Rotating Pendulum (Princeton, Moscow PhysTech) The bearing of a rigid pendulum of mass is forced to rotate uniformly with angular velocity (see Figure P.
1) is the proper time along this worldline. c) Define the acceleration 4-vector for this motion and show that it has constant magnitude. 1), starting at and Also, at she leaves behind a satellite that remains at rest at The satellite emits flashes of light at a rate that is constant in the satellite’s rest frame. Show that only a finite number of flashes ever reach the observer. 1), decides to retrieve the satellite. Show that she cannot wait longer than to decide to do so. Hint: To retrieve it at this limiting time, she must “reach down” to the satellite with the speed of light, bring it back at the speed of light, and wait indefinitely long for its return.
It is connected to a spring fastened to a wall. Initially, the amplitude of the oscillations is and the spring constant of the spring is The spring constant then decreases adiabatically at a constant rate until the value is reached. ) What is the new amplitude? Hint: Use the result of (a). 53 Superball in Weakening Gravitational Field (Michigan State) A superball is bouncing vertically up and down. It has a velocity when it strikes the ground. The acceleration due to gravity is slowly reduced by 10% during a very long period of time.
A Guide to Physics Problems: Mechanics, Relativity, and Electrodynamics by Sidney B. Cahn, Boris E. Nadgorny, C.N. Yang