Lecture13

Lecture13 - Physics 344 Foundations of 21 st Century...

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Unformatted text preview: Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Fan Chen Office: PHYS 222 [email protected] Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! Help Session: Thursdays 2:00 – 4:00 in PHYS 154 Reading: Chapters 1 through 8 in Six Ideas that Shaped Physics, Unit R. Exam 1: Wednesday, October 5 at 8:00pm in WTHR 104 Last lecture we introduced a new way of thinking about and working in spacetime by adapting familiar vector-geometric methods that we use so effectively when working in space. By designating one location in space as an origin, O , we can associate a position vector with every location in space. We examined examples of how we can work algebraically with such vectors to express and analyze geometrical relationships between locations and line segments that connect them. x y Y O X L ˆ ˆ L LO x x x x = ∆ ˆ ˆ L LO y y y y = ∆ ˆ ˆ L LO Y Y Y Y = ∆ ˆ ˆ L LO X X X X = ∆ L r a We can connect this way of working to coordinate methods by choosing coordinate axes and dimensionless unit vectors oriented parallel to them. The coordinates of a location are the components of its position vector. ˆ ˆ L L L r x x y y = + a If we choose a rotated set of coordinate axes, we represent the same vector with a different set of components related to the first ones by rotation transformation equations. ˆ ˆ L L L r X X Y Y = + a θ θ x y Y O X ˆ (1m) sin( ) x θ- ˆ (1m) cos( ) y θ ˆ (1m) B Y = a ˆ (1m) A X = a ˆ (1m) sin( ) y θ ˆ (1m) cos( ) x θ The relationship between the dimensionless unit vectors of two coordinate systems is equivalent to the rotation transformation equations that relate them. Q1. What is the y-component of ? A) (1m)cos( θ ) B) (1m)sin( θ ) C) (1m)tan( θ ) D) (1m) θ θ A a ˆ ˆ ˆ ˆ ˆ ˆ (1m) (1m) cos( ) (1m)sin( ) cos( ) sin( ) X x y X x y θ θ θ θ = + ⇒ = + * Similarly, ˆ ˆ ˆ ˆ ˆ ˆ (1m) (1m)sin( ) (1m) cos( ) sin( ) cos( ) Y x y Y x y θ θ θ θ = - + ⇒ = - + So, ( 29 ( 29 ( 29 ( 29 ˆ ˆ ˆ ˆ ˆ ˆ cos( ) sin( ) sin( ) cos( ) ˆ ˆ ˆ ˆ cos( ) sin( ) sin( ) cos( ) r XX YY X x y Y x y X Y x X Y y xx yy θ θ θ θ θ θ θ θ = + = + +- + =- + + ≡ + a cos( ) sin( ) sin( ) cos( ) x X Y y X Y θ θ θ θ =- = + implies the rotation transformation equations, We saw last time that we could introduce and use spacetime separation 4-vectors in essentially the same way. in essentially the same way....
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This note was uploaded on 12/09/2011 for the course PHYS 344 taught by Professor Garfinkel during the Fall '08 term at Purdue.

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Lecture13 - Physics 344 Foundations of 21 st Century...

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