Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley PowerPoint ® Lectures for University Physics, Twelfth Edition – Hugh D. Young and Roger A. Freedman Lectures by James Pazun Chapter 3 Motion in Two or Three Dimensions

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Position relative to the origin—Figure 3.1 An overall position relative to the origin can have components in x, y, and z dimensions.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Velocidad media e instantánea—Figura 3.2 The average velocity between two points will have the same direction as the displacement.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Aceleración media e instantánea—Figura 3.6 The acceleration vector can result in a change in either the magnitude OR the direction of the velocity.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Componentes perpendicular y paralela a la aceleración. Figura 3.10

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Velocidad y aceleración para una trayectoria curva Partícula que se mueve en una trayectoria curva para tres situaciones diferentes: No hay componente tangencial Hay, tanto componente tangencial como normal

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Projectile motion—Figure 3.15

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Principio de independencia de Galileo—Figure 3.16 La bola roja se deja caer, y la amarilla es lanzada horizontalmente. El estroboscopio señala intervalos de tiempo iguales En un instante dado, ambas bolas tienen igual posición, velocidad y aceleración en el eje VERTICAL. Sin embargo tienen diferente posición y velocidad en el eje HORIZONTAL

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The equations of motion under constant acceleration x = (v o cosα o )tMU y = (v o sinα o )t  1/2gt 2 MUA v x = v o cosα o MU v y = v o sinα o  gtMUA

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Tranquilizing the falling monkey

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Motion in a circle—Figure 3.27 (equivale a 3.12) The vehicle could be speeding up in the curve, slowing down in the curve, or undergoing uniform circular motion.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Movimiento circular uniforme

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Nonuniform circular motion—Figure 3.30

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Relative velocity on a straight road—passing! Mov. Absoluto= Mov. Arrastre + Mov. Relativo Mov. Absoluto es el del Objeto P respecto al SRF (A) Mov. Relativo es el del Objeto P respecto al SRM (B) Mov. Arrastre es el del SRM (B) respecto al SRF (A)

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Relative velocity in two or three dimensions

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Vuelo con viento cruzado. Figure 3.35 La brujula de un avión indica que va hacia el Norte, y su velocímetro indica 240 Km/h. Si hay un viento de 100Km/h de Oeste a Este. ¿Cuál es la velocidad del avión respecto a tierra?

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Angular motions in revolutions, degrees, and radians One complete cycle of 360° is one revolution. One complete revolution is 2 π radians. Relating the two, 360° = 2 π radians or 1 radian = 57.3°.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Angular velocity is a vector

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Angular acceleration is a vector

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Rotación con aceleración angular constante. Relación lineal/angular

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Velocidad lineal de un cuerpo rígido Cuando un sólido rígido gira respecto a un eje fijo, todas sus partículas se mueven en un movimiento circular. Todas las partículas giran el mismo ángulo al unísono (ω=cte), pero dependiendo de su distancia al eje de giro con distinta velocidad líneal

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Aceleración angular de un cuerpo rígido