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.

Some bounds of loss in classical semideterministic immunization

Since Samuelson, Redington and Fisher and Weil, duration and immunization are very important topics in bond portfolio analysis from both a theoretical and a practical point of view. Many results have been established, especially in semi-deterministic framework. As regards, however, the loss may be sustained, we do not think that the subject has been investigated enough, except for the results found in the wake of the theorem of Fong and Vasicek. In this paper we present some results relating to the limitation of the loss in the case of local immunization for multiple liabilities.

Tilted boxes on inclined planes

We propose the study of a box placed on an inclined plane, with an initial tilt with respect to the plane. This is a paradigmatic example of the role played by friction as a link between translational and rotational motion. This example has two advantages over the usual example of a sphere (or cylinder) rolling down an inclined plane. First, it provides a good model for a much greater variety of "real-life" situations. Second, it exhibits a much richer structure in parameter space, even when the box starts from rest. (C) 2000 American Association of Physics Teachers.

De intruso a tutor: impactos da formação em contexto PNEP

Este trabalho decorre de uma experiência de formação contínua de âmbito nacional, durante um ano letivo, relacionada com o ensino do português no 1º Ciclo no contexto do Programa Nacional de Ensino do Português (PNEP). Para se compreender o impacto da formação e do seu modelo, analisaram-se as produções escritas (do género narrativo e epistolar) dos alunos do 1º ao 4º ano de escolaridade, os resultados das Provas de Aferição de Língua Portuguesa do 4º ano, os inquéritos de avaliação dos formandos à própria formação, da competência da Comissão Nacional de Acompanhamento (CNA) e, ainda, as reflexões dos portefólios produzidos pelos formandos ao longo da formação. Em génese, pretende-se aferir de que modo esta formação interferiu nas aprendizagens e no desenvolvimento de competências dos alunos no domínio da língua materna, nomeadamente ao nível da escrita. Nessa perspetiva, são comparados dois grupos de alunos do mesmo agrupamento, do distrito de Lisboa, sendo o grupo experimental constituído pelos alunos cujos professores frequentaram a ação de formação PNEP e o grupo de controlo formado por alunos cujos professores nunca frequentaram a referida ação. Todavia, podendo o PNEP ser considerado como uma formação inovadora, porque se desenvolve em contexto, procura-se também saber como se sentiram os professores ao longo desta formação, bem como que repercussões e mais-valias obtiveram para as suas práticas pedagógicas e para a resolução real dos problemas vividos na sala de aula. Por fim, cruzando todos os dados de que se dispõe, aspira-se compreender o papel e o contributo da figura do formador no contexto PNEP, o que poderá conduzir a uma nova abordagem de formação, mais consentânea com o conceito de “mentoria”, e seus processos, do que com os pressupostos iniciais assentes numa lógica de “tutoria”. - This study originates from a one year education experience, nation wide, in the wake of the PNEP (Programa Nacional de Ensino do Português, in its maiden form) program. The aim is to understand how the model herein impacts first to fourth year primary school children’s learning and writing skills, how it influences the fourth year’s final exam results, and how it is reflected on practitioners’ (teachers undergoing the PNEP) performance evaluation inquires, and on concept development within their portfolios. In genesis, we seek to analyse whether the PNEP changed the way children attending primary school learn and master Portuguese, particularly its written expression. To do so, the study focus on two different publics, whereby an experimental group was build around a set of classes whose teachers had completed the PNEP education and training program, and a control group, set around a similar sample, but where teachers had no PNEP education or training at all. In addition, because PNEP might be considered as an advanced education model, we also wanted to disclosure how it adds to schoolteachers’ education techniques, and how it would help them solve daily ordinary problems within the classroom. Last but not the least, the study reveals that PNEP can change Portuguese standard education perspectives, changing classic tutorial methodologies towards a, more responsive, mentoring approach.