qz7sol_3706Hs11 - is I b =(1/12)ML 2 a What is the...

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TA: Tomoyuki Nakayama Tuesday, March 22, 2011 PHY 2048: Physic 1, Discussion Section 3706H Quiz 7 (Homework Set #9) Name: UFID: Formula sheets are not allowed. Do not store equations in your calculator. You have to solve problems on your own; memorizing final algebraic expressions from homework assignments and just plugging numbers into them will not give you full credit. Leave all your work. ________________________________________________________________________________ The figure below right shows a rigid structure consisting of a circular hoop of diameter D = 1.40 m (radius R = 0.700 m) and mass m = 2.00 kg, and a square made of four thin bars, each of length L = 0.800 m and mass M = 1.50 kg. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 5.00 s. The rotational inertia of a hoop about an axis through its diameter is I h = (1/2)mR 2 , and that of a bar about an axis passing through its center perpendicularly to the bar
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Unformatted text preview: is I b = (1/12)ML 2 . a) What is the rotational inertia of the rigid structure about the rotational axis? Since the structure consists of a hoop and square, the total rotational inertia is I tot = I H + I S According to the parallel axis theorem, the rotational inertia of the hoop about the axis through its rim is I H = (1/2)mR 2 + mR 2 = (3/2)mR 2 = 1.47 kg · m 2 The square consists of a rod along the axis, two rods with the axis at one end and a rod a distance L away from the axis. The parallel axis theorem yields I S = 0 + 2 × [(1/12)ML 2 + (1/2)ML 2 ] + ML 2 = (5/3)ML 2 = 1.60 kg · m 2 The rotational inertia of the structure is I tot = I H + I S = 3.07 kg · m 2 b) What is the angular momentum about the rotational axis? The angular velocity of the structure is ω = 2 π /T = 1.26 rad/s By definition, the angular momentum of the structure is l = I tot ω = 3.86 kg · m 2 /s...
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This note was uploaded on 12/10/2011 for the course PHY 2048 taught by Professor Field during the Spring '08 term at University of Florida.

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