Abstract
This paper deals with an effect which appears when heating or cooling a rotating body. No external forces acting on the body are supposed. Due to thermal expansion, the moment of inertia of the body varies together with the temperature changes. In agreement with the principle of conservation of angular momentum [1], the angular momentum is constant. This results in angular velocity changes and subsequently in kinetic energy changes. Also the stress energy varies together with the changes in thermal dimension. To satisfy the principle of energy conservation we have to suppose that the changes in kinetic and stress energy are compensated by the changes in internal energy, which is correlated with temperature changes of the body. This means that the rules for the heating or cooling process of a rotating body are not the same as those for a body at rest. This idea, applied to a cylinder rotating around its geometric axis under specific parameters, has been mathematically treated. As a result, the difference between the final temperature of the rotating cylinder and the temperature of the cylinder at rest has been found.
Highlights
If a rotating body is heated, its internal energy increases and the concurrent temperature increase is followed by thermal expansion
Since the angular momentum of the body is proportional to the moment of inertia and to the angular velocity [1], the increase in the moment of inertia is followed by a reduction in angular velocity
The final effect is that there is a decrease in the kinetic energy of the rotating body, which is proportional to the moment of inertia and to the power in the angular velocity. (An example of a converse effect is the increase of the angular velocity of a “black hole” during its gravitational collapse)
Summary
If a rotating body is heated, its internal energy increases and the concurrent temperature increase is followed by thermal expansion. This results in an increase in the moment of inertia of the body. As proved by the following mathematical calculation, deformation energy decreases with thermal expansion This means that the deficit of kinetic energy and of deformation energy converts into an increase in the internal energy of the body. The elastic deformation of the body originating from centrifugal forces is very small in comparison with the thermal expansion, and its dependence on angular velocity is neglected
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