Angular and linear accelerations of a rolling cylinder acted by an external force

The dynamics of a cylinder rolling on a horizontal plane acted on by an external force applied at an arbitrary angle is studied with emphasis on the directions of the acceleration of the centre-of-mass and the angular acceleration of the body. If rolling occurs without slipping, there is a relationship between the directions of these accelerations. If the linear acceleration points to the right, then the angular acceleration is clockwise. On the other hand, if it points to the left, then the angular acceleration is counterclockwise. In contrast, if rolling and slipping occurs, the direction of the linear acceleration does not determine the direction of the angular acceleration. For example, the linear acceleration may point to the right and the angular acceleration clockwise or counterclockwise depending on the external force orientation and point of application.

Comparing a current-carrying circular wire with polygons of equal perimeter: Magnetic field versus magnetic flux

We compare the magnetic field at the centre and the self-magnetic flux through a current-carrying circular loop, with those obtained for current-carrying polygons with the same perimeter. As the magnetic field diverges at the position of the wires, we compare the self-fluxes utilizing several regularization procedures. The calculation is best performed utilizing the vector potential, thus highlighting its usefulness in practical applications. Our analysis answers some of the intuition challenges students face when they encounter a related simple textbook example. These results can be applied directly to the determination of mutual inductances in a variety of situations.

Comparing wind generation profiles: A circular data approach

The importance of wind power energy for energy and environmental policies has been growing in past recent years. However, because of its random nature over time, the wind generation cannot be reliable dispatched and perfectly forecasted, becoming a challenge when integrating this production in power systems. In addition the wind energy has to cope with the diversity of production resulting from alternative wind power profiles located in different regions. In 2012, Portugal presented a cumulative installed capacity distributed over 223 wind farms [1]. In this work the circular data statistical methods are used to analyze and compare alternative spatial wind generation profiles. Variables indicating extreme situations are analyzed. The hour (s) of the day where the farm production attains its maximum daily production is considered. This variable was converted into circular variable, and the use of circular statistics enables to identify the daily hour distribution for different wind production profiles. This methodology was applied to a real case, considering data from the Portuguese power system regarding the year 2012 with a 15-minutes interval. Six geographical locations were considered, representing different wind generation profiles in the Portuguese system.In this work the circular data statistical methods are used to analyze and compare alternative spatial wind generation profiles. Variables indicating extreme situations are analyzed. The hour (s) of the day where the farm production attains its maximum daily production is considered. This variable was converted into circular variable, and the use of circular statistics enables to identify the daily hour distribution for different wind production profiles. This methodology was applied to a real case, considering data from the Portuguese power system regarding the year 2012 with a 15-minutes interval. Six geographical locations were considered, representing different wind generation profiles in the Portuguese system.