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Unformatted text preview: roofner (bar784) – Homework 15 – Weathers – (17104) 1 This printout should have 12 questions. Multiplechoice 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 ω 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 ω 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 ω 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 = ℓ sin θ . Let : ℓ = 2 m , θ = 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 θ Solution: The second Newton’s law in the vertical and horizontal projections, respec tively, in our case reads T cos θ m g = 0 T sin θ m ω 2 ℓ sin θ = 0 , where T is the force with which the wire acts on the bob and the radius of the orbit is R = ℓ sin θ . From this system of equations we find ω = radicalbigg g ℓ cos...
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 Fall '08
 Weathers
 mechanics, Angular Momentum, Work, Ri, Lafter, Lbefore, mmin lmin

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