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Unformatted text preview: roofner (bar784) Homework 15 Weathers (17104) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 2) 10.0 points The hour and minute hands of Big Ben in London are 2 . 74 m and 4 . 44 m long and have masses of 69 . 6 kg and 95 kg respectively. Calculate the total angular momentum of the minute hand about the center point. Treat the hand as long, thin rod. Treat into the clock as the positive direction. Correct answer: 1 . 08955 kg m 2 / s. Explanation: Basic Concepts: L = I Moment of inertia of a thin rod pivoted through one of its ends is I = m l 2 3 , where m is its mass and l is its length. Solution: Applying this formula to the minute hand we obtain its moment of inertia: I min = m min l 2 min 3 = (95 kg)(4 . 44 m) 2 3 = 624 . 264 kg m 2 The angular momentum is L min = I min min = ( 624 . 264 kg m 2 ) (0 . 00174533 1 / s) = 1 . 08955 kg m 2 / s 002 (part 2 of 2) 10.0 points Calculate the total angular momentum of the hour hand about the center point. Treat the hand as long, thin rod, and into the clock as the positive direction. Correct answer: 0 . 0253329 kg m 2 / s. Explanation: This part is to be solved similarly to the previ- ous part. We obtain for the moment of inertia of the hour hand: I hr = m hr l 2 hr 3 = (69 . 6 kg)(2 . 74 m) 2 3 = 174 . 176 kg m 2 The angular momentum is L hr = I hr hr = (174 . 176 kg m 2 )(0 . 000145444 1 / s) = 0 . 0253329 kg m 2 / s 003 10.0 points A small metallic bob is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal circle so that the thread describes a cone. The acceleration of gravity is 9 . 8 m / s 2 . v 9 . 8 m / s 2 2 m 5 kg 3 3 Calculate the magnitude of the angular momentum of the bob about the support- ing point. Correct answer: 14 . 34 kg m 2 / s. Explanation: Basic Concepts: Angular Momentum L = m vectorr vectorv . Note: In this problem vectorr and vectorv are perpendic- ular, where r = sin . Let : = 2 m , = 33 , g = 9 . 8 m / s 2 , and m = 5 kg . roofner (bar784) Homework 15 Weathers (17104) 2 Use the free body diagram below. T m g Solution: The second Newtons law in the vertical and horizontal projections, respec- tively, in our case reads T cos - m g = 0 T sin - m 2 sin = 0 , where T is the force with which the wire acts on the bob and the radius of the orbit is R = sin . From this system of equations we find = radicalbigg g cos...
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