Phys205A_Lecture6

Physics for Scientists & Engineers with Modern Physics (4th Edition)

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 6 Chapter 3 Vectors
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Coordinate Systems z Used to describe the position of a point in space z Coordinate system consists of z A fixed reference point called the origin z Specific axes with scales and labels z Instructions on how to label a point relative to the origin and the axes
Background image of page 2
Cartesian Coordinate System z Also called rectangular coordinate system z x - and y - axes intersect at the origin z Points are labeled ( x , y )
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Polar Coordinate System z Origin and reference line are noted z Point is distance r from the origin in the direction of angle θ , ccw from reference line z Points are labeled ( r , )
Background image of page 4
Polar to Cartesian Coordinates z Based on forming a right triangle from r and θ z x = r cos z y = r sin
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Trigonometry Review z Given various radius vectors, find z Length and angle z x- and y-components z Trigonometric functions: sin, cos, tan
Background image of page 6
Cartesian to Polar Coordinates z r is the hypotenuse and θ an angle z must be ccw from positive x axis for these equations to be valid 22 tan y x rxy θ= =+
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 3.1 z The Cartesian coordinates of a point in the xy plane are ( x,y ) = (-3.50, -2.50) m, as shown in the figure. Find the polar coordinates of this point. Solution: From Equation 3.4, and from Equation 3.3, 22 2 2 ( 3.50 m) ( 2.50 m) 4.30 m rxy =+ = + = 2.50 m tan 0.714 3.50 m 216 (signs give quadrant) y x θ == =
Background image of page 8
Example 3.1, cont. z Change the point in the x-y plane z Note its Cartesian coordinates z Note its polar coordinates Please insert active fig. 3.3 here
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Vectors and Scalars z A scalar quantity is completely specified by a single value with an appropriate unit and has no direction. z A vector quantity is completely described by a number and appropriate units plus a direction.
Background image of page 10
Vector Example z A particle travels from A to B along the path shown by the dotted red line z This is the distance traveled and is a scalar z The displacement is the solid line from A to B z The displacement is independent of the path taken between the two points z Displacement is a vector
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Vector Notation z Text uses bold with arrow to denote a vector: z Also used for printing is simple bold print: A z When dealing with just the magnitude of a vector in print, an italic letter will be used: A or | | z The magnitude of the vector has physical units z The magnitude of a vector is always a positive number z When handwritten, use an arrow: A r A r A r
Background image of page 12
Equality of Two Vectors z Two vectors are equal if they have the same magnitude and the same direction z if A = B and they point along parallel lines z All of the vectors shown are equal = AB rr
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Adding Vectors z When adding vectors, their directions must be taken into account z Units must be the same z Graphical Methods z Use scale drawings z Algebraic Methods z More convenient
Background image of page 14
Image of page 15
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 09/27/2011.

Page1 / 45

Phys205A_Lecture6 - Lecture 6 Chapter 3 Vectors Coordinate...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online