p4 - i d | r t | dt ii v t ˆ r t where ˆ r is the unit...

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Physics 21 Problem Set 4 Harry Nelson due Monday, February 5, In Class Course Info: The reading this week will be: 1)Review pp. 52-75 (Chapter 2), 2)pp. 23-38 (Chapter 1). Prof. Nelson’s office hours: Friday 2-2:50pm 5103 Broida, 4:10-5:30pm in Phelps 1508. Richard Eager’s office hours are Monday 2:00-3:00pm, Tuesday 11:00-12:00noon, and Thursday 11:00-12:00noon in Broida 1019 (The Physics Study Room). 5. Consider again motion in an elliptical path, r ( t ) = a cos( ωt ı + b sin( ωt (a) Compute ˙ r two different ways, and check to see if you get the same answer:
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Unformatted text preview: i. d | r ( t ) | dt ii. v ( t ) · ˆ r ( t ), where ˆ r is the unit vector constructed from r ( t ). This manner of calculating ˙ r is geometric (see the figure on page 33), and uses the first term of problem 1.11 of K&K. (b) The other component of the velocity, from the figure on page 33, is r ˙ θ ˆ θ . This component, according to problem 1.11, should also be (ˆ r ( t ) × v ( t )) × ˆ r ( t ). Evaluate (ˆ r ( t ) × v ( t )) × ˆ r ( t ), and show from its magnitude that: | ˙ θ | = ab a 2 cos 2 ( ωt ) + b 2 sin 2 ( ωt ) | ω | . What happens when a = b ?...
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