Thursday, April 23, 2009

Irodov Problem 1.309

The volume density of energy due to elastic deformation is given by . So the volume of the steel rod is V, then the total energy in the steel rod is given by . If the mass of the steel rod is m then we can rewrite it as.

Irodov Problem 1.308















Consider an infinitesimally thin ring section of radius r and thickness dr. The mass of this thin ring section is given by where p is the density of the ring. Each point in this thin ring section experiences a tangential linear acceleration of . When viewed from the reference frame fixed to the ring, this translates to a pseudo force . This pseudo force translates to a pseudo torque . The net torque is then given by,