Solutions to I E Irodov - Physical Fundamentals of Mechanics

Newton single handedly brought about a new era in our understanding of the physical world, through his famous equation F = ma and the law of gravity. These laws successfully predict the behavior of all phenomena from the microscopic world to the astronomical world! Ofcourse, Einstien changed things once again but that was only after about 4 centuries. Solving Irodov dramatically helped me understand the power, elegance, simplicity and beauty of Physics. Hopefully you will enjoy the journey too.

Wednesday, April 8, 2009

Irodov Problem 1.296

Consider an infinitesimally small piece of the rod at a distance r (point X) from the axis of rotation of length dr. If the density of the material is p and surface area of cross-section of the rod is S, then the mass of the infinitesimally small piece of rod will be pSdr. The centrifugal force experienced by this infinitesimally small piece will be

.

Let the force with which the part of the rod XB pulls the part AX with a force f(r) given by,

The stress is thus given by,

The strain is thus given by,

Suppose that the part XB was stretched by

due to the rotation, then we have,

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