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Homework 16

# Homework 16 - Gozick Brandon – Homework 16 – Due Nov 7...

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Unformatted text preview: Gozick, Brandon – Homework 16 – Due: Nov 7 2006, 7:00 pm – Inst: D Weathers 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 2) 10 points A particle of mass 0 . 11 kg is attached to the 100-cm mark of a meter stick of mass . 11 kg. The meter stick rotates on a horizon- tal, frictionless table with an angular speed of 2 . 5 rad / s. Calculate the angular momentum of the system when the stick is pivoted about an axis perpendicular to the table through the 50-cm mark. Correct answer: 0 . 0916667 kg m 2 / s. Explanation: L = Iω The moment of inertia of the stick is I s = 1 12 m s (1 m) 2 and of the particle at- tached to the stick I p = m p µ 1 2 m ¶ 2 . The total moment of inertia of the system is I 1 = I s + I p = 1 12 (0 . 11 kg) (1 m) 2 + (0 . 11 kg) µ 1 2 m ¶ 2 = 0 . 0366667 kg m 2 , and the angular momentum is L 1 = I 1 ω = (0 . 0366667 kg m 2 )(2 . 5 rad / s) = 0 . 0916667 kg m 2 / s . 002 (part 2 of 2) 10 points Calculate the angular momentum of the sys- tem when the stick is pivoted about an axis perpendicular to the table through the 0-cm mark. Correct answer: 0 . 366667 kg m 2 / s. Explanation: The moment of inertia of the stick in this case is I s = 1 3 m s (1 m) 2 and of the particle attached to the stick I p = m p (1 m) 2 . The total moment of inertia of the system is I 2 = I s + I p = 1 3 (0 . 11 kg) (1 m) 2 + (0 . 11 kg (1 m) 2 = 0 . 146667 kg m 2 , and the angular momentum is L 2 = I 2 ω = (0 . 146667 kg m 2 )(2 . 5 rad / s) = 0 . 366667 kg m 2 / s . keywords: 003 (part 1 of 1) 10 points A solid cylinder of mass M = 14 kg, radius R = 0 . 48 m and uniform density is pivoted on a frictionless axle coaxial with its symmetry axis. A particle of mass m = 1 . 4 kg and initial velocity v = 15 m / s (perpendicular to the cylinder’s axis) flies too close to the cylinder’s edge, collides with the cylinder and sticks to it. Before the collision, the cylinder was not ro- tating. What is its angular velocity after the collision? Correct answer: 5 . 20833 rad / s. Explanation: Basic Concept: Conservation of Angu- lar Momentum, L particle z + L cylinder z = const ....
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Homework 16 - Gozick Brandon – Homework 16 – Due Nov 7...

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