A Guide to Physics Problems. part 12 Mechanics, Relativity, by S.Cahn, B.Nadgorny

By S.Cahn, B.Nadgorny

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C) For what is the stable equilibrium value of d) What is the frequency of small oscillations about this point? 33. Two balls, each of mass are attached by means of four hinged arms, each of length to sleeves on a vertical rod. The upper sleeve is fastened to the rod; the lower sleeve has mass M and is free to slide up and down the rod as the balls move out from or in toward the rod. The rod-and-ball system rotates with constant angular velocity 20 PROBLEMS a) Set up the equation of motion, neglecting the weight of the arms and rod.

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. , the rectilinear motion) for which the acceleration in the proper reference frame (at each instant of time) remains constant. a) Show that the 4-velocity b) Show that the condition for such a motion is where is the usual three dimensional acceleration. 10). RELATIVITY 39 a) Write the relativistic equations for momentum and energy conservation.

47 Shallow Water Waves (Princeton (a,b)) Water waves travel on the surface of a large lake of depth The lake has a perfectly smooth bottom and the waves are propagating purely in the direction (The wave fronts are straight lines parallel to the axis. See Figure P. 47). a) Find an expression for the velocity of the water b) Find the corresponding dispersion relation. You may assume that the flow of the water is irrotational that the amplitude of the waves is small (in practice, this means that where is the MECHANICS 29 height of the waves), that surface tension effects are not important, and that water is incompressible.

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