P5 - a cos t i a sin t j and confirm that this agrees with...

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Math 241, Problem Set #5 (due in class Fri., 10/7/11) Stewart, section 10.8, problems 10, 18, 24, 30, 44. Stewart, section 10.9, problems 18, 22, 32, 34. Also: A. Recall that in the metric system of measurement, position has units of meters and time has units of seconds. Determine the metric unit unit of curvature, using the formula (9) on page 572. Do the same with formula (10) on page 573 and check that you get the same answer. Explain why this answer makes sense with respect to the geometrical interpretation of curvature. B. Apply formula (10) to the circle (
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Unformatted text preview: a cos t ) i + ( a sin t ) j and confirm that this agrees with the geometric interpretation of the curvature as the reciprocal of the radius of the osculating circle. C. Compute the curvature of the helix h cos t, sin t,t i . (Hint: Before you dive in and compute a parametrization of the curve by arc-length, see if one of the formulas for curvature gives us the answer with less work.) D. Consider the curve r ( t ) = h e-t cos t,e-t sin t,e-t i , t ≥ 0. Compute the curvature and show that it goes to infinity as t → ∞ ....
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