HW22_Solutions - hiarker(srh959 homework 22 Turner(58220 This print-out should have 11 questions Multiple-choice questions may continue on the next

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hiarker (srh959) – homework 22 – Turner – (58220) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points A uniForm rod oF mass 2 . 6 kg is 21 m long. The rod is pivoted about a horizontal, Frictionless pin at the end oF a thin extension (oF negligible mass) a distance 21 m From the center oF mass oF the rod. Initially the rod makes an angle oF 51 with the horizontal. The rod is released From rest at an angle oF 51 with the horizontal, as shown in the fgure. 21 m 21 m 2 . 6 kg O 51 What is the angular speed oF the rod at the instant the rod is in a horizontal position? The acceleration oF gravity is 9 . 8 m / s 2 and the moment oF inertia oF the rod about its center oF mass is I cm = 1 12 mℓ 2 . Correct answer: 0 . 818255 rad / s. Explanation: Let : = 21 m , θ = 51 , and m = 2 . 6 kg . Rotational kinetic energy is K R = 1 2 I ω 2 and gravitational kinetic energy is K trans = mg d . The inertia oF the system is I = I cm + md 2 = 1 12 mℓ 2 + mℓ 2 = 13 12 mℓ 2 . Since the rod is uniForm, its center oF mass is located a distance From the pivot. The vertical height oF the center oF mass above the horizontal is sin θ . Using conservation oF energy, K i + U i = K f + U f K f = U i 1 2 I ω 2 = mg ℓ sin θ 13 24 mℓ 2 ω 2 = mg ℓ sin θ ω 2 = 24 13 g sin θ ω = r 24 g sin θ 13 = R 24 (9 . 8 m / s 2 ) sin 51 13 (21 m) = 0 . 818255 rad / s . keywords: 002 10.0 points A circular-shaped object oF mass 15 kg has an inner radius oF 13 cm and an outer radius oF 30 cm. Three Forces (acting perpendicular to the axis oF rotation) oF magnitudes 13 N, 27 N, and 13 N act on the object, as shown. The Force oF magnitude 27 N acts 31 below the horizontal. 13 N 13 N 27 N 31 ω
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hiarker (srh959) – homework 22 – Turner – (58220) 2 Find the magnitude of the net torque on the wheel about the axle through the center of the object. Correct answer: 4
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This note was uploaded on 04/23/2010 for the course PHY 303K taught by Professor Nui during the Spring '09 term at University of Texas-Tyler.

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HW22_Solutions - hiarker(srh959 homework 22 Turner(58220 This print-out should have 11 questions Multiple-choice questions may continue on the next

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